Guiding Ideas in Faraday’s Work

(September 22, 1791 — August 25, 1867)

(On the Centenary of the Discovery of Electromagnetic Induction)

Ig. Tamm, Moscow.

Despite the abundance of literature devoted to Faraday—only a small part of which is covered by the list appended at the end of this article—Faraday’s work constitutes an extensive and rewarding field for research. The fundamental problems that characterized the development of physics in the nineteenth century, to a very considerable extent—with the possible exception only of the problems of statistical physics—go back in their origins to Faraday’s work. Yet to this day there is still no sufficiently complete and exhaustive analysis of the evolution of Faraday’s basic ideas, which guided him in his investigations; of the evolution of the conception of electromagnetic forces that he created; of the role that these ideas and conceptions played in Faraday’s discoveries; of his unsurpassed experimental methodology; and, finally, of the interaction between Faraday’s work and the development of technology contemporary with him. Meanwhile, Faraday’s numerous scientific papers, written with extraordinary fullness and leading the reader step by step through all the stages of his investigations, together with his abundant literary legacy in the form of diaries, letters, notes, lectures, speeches, and so on, constitute exceptionally valuable material both for resolving these questions and for studying the mechanism and distinctive features of scientific creativity in general. From the beginning of the twenties to

from the sixties of the last century onward, Faraday kept the most detailed laboratory notes, or “Diary,” in which he entered all the details of his experiments, plans and proposals for future work, analysis of results, discussion of difficulties encountered, and hopes for the future. The separate sheets on which these notes were made were later bound—mostly by Faraday himself, a master bookbinder—into 8 volumes in folio and 2 volumes in quarto. In the literature only individual excerpts from the “Diary” have so far been published, but in connection with the celebration of the anniversary of the law of induction a complete edition of this valuable material has at last been undertaken.

The beginning of the second, most fruitful period of Faraday’s activity, which alone we shall touch upon in the present article, coincides with the fortieth year of his life and with the beginning of the publication of the famous Experimental Researches in Electricity (“Experimental investigations in electricity”). From 1831 to 1855 these “Researches” appeared regularly in Philosophical Transactions*. Set out in the form of short paragraphs, the number of which in 30 “series,” or papers, reached 3362, containing not a single mathematical formula or mathematical exposition, but describing with extraordinary thoroughness the details of experiments and comprising an exhaustive, exceptionally clear, and profound analysis of physical phenomena and concepts, these researches constitute the quintessence of Faraday’s scientific legacy.

* Thus Faraday represents a comparatively rare example of a late-developing genius, and it remains debatable whether this is to be explained chiefly by the peculiarities of his mental organization or by the fact that, being a self-taught workman, he did not have sufficiently favorable conditions for development in childhood and youth. The stages of the first period of his activity up to 1831—his first scientific work was published in 1816—are characterized by a series of works on analytical and technical chemistry, on the liquefaction of chlorine and other gases, studies in acoustics, and the carrying out of continuous rotation of a current-carrying conductor in the field of magnets (Faraday’s wheel). The significance of these works cannot bear any comparison with the discoveries of the second period of his activity.

Using chiefly these Experimental Researches,* and without claiming any completeness of exposition, in the present article we shall attempt, in the most general outline, to consider Faraday’s most important discoveries in connection with the question of what role in these discoveries was played, as a guiding element, by Faraday’s general methodological attitude and, above all, by the two fundamental ideas that guided him—the idea of the unity of the forces of nature and the new conception of electromagnetic phenomena that he created. General attitudes of this kind played an extraordinarily important role in most major discoveries of the class for which the German language has the very apt term epochemachend (epoch-making). Discoveries such as, for example, the discovery of X-rays, which occurred by chance, are in this respect exceptions that only confirm the general rule. When the matter concerns the investigation of phenomena whose basic properties and laws are already known, or the application of known laws to new phenomena, the investigator’s general methodological, philosophical attitude does not play so essential a role. But when the matter concerns the discovery of new phenomena and the laws governing them, the discovery of new properties of nature, success can be ensured only by the presence of a definite guiding thread. And if Columbus did not, of course, have an exact idea of what awaited him ahead, he nevertheless had a firm certainty as to the direction in which it was necessary to steer in order to reach a new land.

This conviction in the correctness of the chosen path, the astonishing persistence with which Faraday again and again returned to experiments that had disappointed his expectations, varying their conditions in every possible way, are extraordinarily characteristic of Faraday. We shall confine ourselves to one of many examples—the discovery of the rotation of the plane of polarization of light in a magnetic field. Here is what he himself wrote on this

* Hereafter references to them will be given in the form “Exp. Res.”, with the number of the corresponding paragraph indicated.

concerning this in 1845: “I have long held an opinion, which has almost reached the degree of conviction, that the various forms in which the forces of matter manifest themselves have one common origin, or, in other words, are so directly connected and dependent upon one another that they can, as it were, be transformed into one another, and that there exist equivalents of their action. This firm conviction, when applied to the actions of light, led me in the past to many attempts aimed at discovering a direct connection between light and electricity and their interaction when acting jointly upon bodies; however, the results proved negative. These unsuccessful efforts, and many others about which nothing was ever published, could not remove my firm conviction, arising from philosophical considerations. Therefore I have recently resumed the most careful investigations by experiment, and at last I have succeeded in magnetizing and electrifying a ray of light and in illuminating magnetic lines of force”*. Records of the unsuccessful preliminary attempts mentioned by Faraday in 1845 are found in his working diary, relating to 10 September 1822 and to 2 and 6 May 1833. And finally, the last experiment of his life (entry of 12 March 1862) was also undertaken with the aim of detecting new forms of connection between light and magnetism, and only the imperfection of the instruments at his disposal prevented Faraday from discovering on that day the Zeeman effect, who successfully repeated this experiment with better experimental means in 1896. Thus, over the course of forty years Faraday returned again and again to the very same question of the connection between light and electromagnetism, despite both failures and partial successes.

The conviction of the unity of the forces of nature, so vividly expressed in the words of Faraday quoted above, guided him throughout all his activity. To appreciate the importance of this idea, it is necessary to recall the state of physics in that

* “Expl. Res.”, Nos. 2146–2148 (emphasis ours. I. T.).

epoch. By the end of the eighteenth and the beginning of the nineteenth century, the domain of known physical phenomena had expanded considerably; however, these phenomena were studied in isolation from one another, and to explain each group of phenomena recourse was had to the hypothesis of a special “fluid” (substance)—electric fluid, magnetic fluid, caloric, and finally light particles, introduced to explain optical phenomena. As a reaction against this abundance of diverse forces and heterogeneous fluids, the idea arose of the unity of the forces of nature. The idealistic philosophy of Schelling, which prevailed at the beginning of the nineteenth century, contained within itself a sound core of the doctrine of the unity of all the forces of nature and in this direction exerted a significant influence on the development of science. Thus, for example, Ørsted was a convinced Schellingian and came to his famous discovery of the action of an electric current on a magnetic needle not at all by chance, as is sometimes stated, but as the result of many years of persistent searches for the interaction of electricity and magnetism, in the existence of which he was convinced on the basis of philosophical considerations. The crown of this period in the development of physics, characterized by the idea of the unity of the forces of nature, was the establishment of the law of conservation of energy by Robert Mayer, Joule, and Helmholtz.

Let us consider, then, from the point of view of the development of this idea, some of Faraday’s principal works, without adhering strictly to chronological order.

At that time at least five distinct kinds of electricity were distinguished according to the method of obtaining them, namely: a) “ordinary” electricity, which included first and foremost frictional electricity, then atmospheric electricity, piezo- and pyroelectricity; b) galvanic electricity—currents produced by a galvanic battery; c) magnetic electricity—the induction currents discovered by Faraday; d) thermoelectricity; and e) animal electricity, produced by special organs of certain animals (electric rays, eels, etc.). Although at that time the idea of the identity of all these kinds of electricity was already widespread, nevertheless, for example,

Dr. Davy (brother of the famous chemist Humphry Davy) was still writing in 1832 in Phil. Trans. Roy. Society: “May we not suppose, by analogy with the sunbeam, that electricity... is not a simple force, but a combination of different forces capable of occurring in various combinations and thereby producing all the varieties of electricity with which we are familiar?”

Faraday’s work, reported in January 1833, definitively removed all these doubts and established, by means of experiments planned and carried out in exemplary fashion, that all the known effects of electricity—physiological, thermal, chemical, magnetic, mechanical, and luminous—can be obtained with electricity of any origin and that, consequently, all kinds of electricity are identical, while the difference in their actions reduces, first, to the quantity of electricity and, second, to its tension (potential).

Of still greater importance, of course, was Faraday’s fundamental discovery—the discovery of electromagnetic induction. The discovery by Oersted and Ampère in 1819–1821 of ponderomotive forces of interaction between currents and magnets, and the invention of electromagnets, led Faraday to suppose that if a current can excite magnetism, then magnetism in general, and the magnetic field of currents themselves in particular, must in turn be capable of exciting currents. On the other hand, the analogy with the electrostatic induction of charges strengthened Faraday’s conviction of the existence of induction of currents: static electricity induces charges of the opposite sign on neighboring bodies; do currents not also possess an analogous property? As early as 1822 he entered in his notebook: “Convert magnetism into electricity.” The first record of experiments undertaken in order to carry out this program dates from December 28, 1824, and thereafter, with the persistence characteristic of Faraday, he repeatedly returned to them over the course of seven years (in 1825, 1828, and 1831).

The long series of failures was explained by the fact that Faraday at first supposed that a constant current should indu-

...to induce the same constant current in adjacent conductors, and that placing a stationary magnet inside a coil traversed by a current should affect the strength of this current. Only on August 29, 1831, while experimenting with a prototype of the modern transformer (two windings wound side by side on an iron ring), did he discover the induction of currents in one of the windings when the current in the other was made and broken. Thus Faraday did indeed find the connection between electricity and magnetism, but not quite in the form he had supposed. In a very short time after this discovery he investigated most thoroughly both the induction of currents by alternating currents and their induction during the relative motion of a conductor in the field of magnets, and established that the induction of currents depends on the conductor’s cutting of magnetic lines of force. The full clarification of the precise quantitative relationships required considerably more time, and only in 1851 do we find the completed formulation of the law of induction: “Whether a wire cuts lines of force perpendicularly or at an angle, in one direction or in another, it sums the forces

Fig. 1. Faraday’s instruments with which he carried out his first successful experiments in electromagnetic induction.

...corresponding “intersected by them lines,” so that “the quantity of electricity set in motion (thrown in the current) is directly proportional to the number of intersected lines”*.

From the study of the connection between magnetism and electricity, Faraday turned to the study of the connection between chemical and electrical phenomena. The conviction of the unity of these phenomena was widespread in that epoch, and Faraday himself refers to the “remarkable theory proposed by Sir Humphry Davy and developed (illustrated) by Berzelius and other outstanding scientists, according to which ordinary chemical affinity is a simple result of the electrical attraction of particles of matter”**. However, only Faraday succeeded in establishing the exact quantitative laws of electrochemical phenomena, which still bear his name. Having proved in the above-mentioned work of 1832 on the identity of the different kinds of electricity that, in electrolysis, the amount of decomposed substance is proportional to the amount of electricity that has passed through the electrolyte***, Faraday in 1833 subjected the phenomena of electrolysis to a thorough and exhaustive investigation, as a result of which it was established that the quantities of different substances liberated from different electrolytes at a given current strength are proportional to the chemical equivalents of these substances. The discovery of this law, of course, greatly strengthened the position of the supporters of the electrical theory of chemical affinity and enabled Faraday to formulate the foundations of this theory in the following way: “The [chemical] equivalent weights of different bodies are simply equal to the quantities of these bodies possessing equal quantities of electricity or equal electric forces; electricity determines the equivalent numbers, because it determines the forces of affinity” (No. 869). “The forces called chemical affinity and electricity are identical” (No. 918). These facts and propositions—

* Exp. Res., Nos. 3082 and 3115.
** Exp. Res., No. 703.
*** Exp. Res., No. 377.

...are not at all self-evident consequences of the basic conception of the electrical nature of chemical forces; on the contrary, they proved to be in irreconcilable contradiction with the views of Faraday’s contemporary, the leading representative of this standpoint—the renowned Berzelius, according to whom every atom possesses both positive and negative poles, and only the relation between the forces of these poles differs in the atoms of different substances. Having no opportunity to go into these questions in greater detail, let us merely recall that the doctrine of the electrical nature of chemical forces, which was unable to embrace the whole diversity of chemical phenomena, was completely abandoned in the second half of the nineteenth century, only to be revived again toward the end of the century in connection with the study of electrolytic dissociation and electronic phenomena. However, a firm foundation for this doctrine was created only by the modern development of quantum mechanics, which for the first time made it possible to explain chemical bonds of a nonpolar (homeopolar) character by means of exchange forces between electrons (Austauschkräfte), i.e., forces of specifically quantum origin.

All these remarkable investigations and discoveries were made by Faraday over the course of three years, in 1831–1834. The extremely strenuous work undermined his health, and in 1835–1836 there began one of those periods of decline in strength which later, with ever increasing intensity and with diminishing intervals, interrupted his creative activity. Faraday’s next work (on the properties of dielectrics, 1837) belongs rather to the second than to the first of the principal cycles of his work mentioned above. Remaining for the moment, however, within the circle of questions concerning the unity of the forces of nature, we must dwell once more on the already mentioned discovery of the rotation of the plane of polarization of light when a ray passes along the lines of force of a magnetic field (1845), and on the conclusions Faraday drew from this discovery.

In one of the lectures delivered by Faraday in 1816, the following passage occurs: “At the present time, use...

is apparently gaining general acceptance: that light consists of the smallest “atoms” of matter of octahedral shape (sic! I. T.), possessing polarity and differing in their dimensions or velocities”*. What a distance there is from these views to the following, for example, assertion (1846): “According to a view which I venture to express, radiation is the highest form of oscillations of the lines of force which, as is known, connect particles with one another, as well as masses of matter. This view seeks to eliminate the ether, but not oscillations”**. What is essential here is not so much the elimination of the concept of the ether as the idea that the same lines of force by which, according to Faraday’s views, electrical, magnetic, and gravitational phenomena are conditioned, are also the carriers of luminous phenomena. And several years later (in 1851) Faraday, considering the question of the transmission of magnetic forces at a distance, expresses the thought that this transmission may be effected by the luminiferous ether, for, he says, “it is by no means improbable, if the [luminiferous] ether exists at all, that it has other functions besides the simple conveyance of radiation”***.

Of course, this is still very far from a completed electromagnetic theory of light, but nevertheless Faraday quite clearly expressed the conviction not only of the influence of magnetism upon luminous phenomena—which, as the result of long searches, had been established by him—but also of a far deeper kinship of these phenomena in essence.

However, in attempting to discover interactions and to establish the unity of the forces of nature, Faraday did not confine himself to electricity, magnetism, chemical forces, and light; in the last decades of his life he devoted more and more attention to the forces of gravitation. “The long-standing and constant conviction that all the forces of nature depend upon one another and have one common origin or, more precisely, constitute different manifestations of one funda-

* Bence Jones, Life a. lettres of Faraday, V. 1, p. 216.
** Thoughts on ray vibrations, Phil. Mag., 28, 3, 1846.
*** “Exp. Res.”, No. 3075.

mental force, often led me to reflect on the possibility of experimentally establishing a connection between gravitation and electricity and, in this way, including gravitation in the group of such numerous and such varied manifestations of forces, embracing also magnetism, chemical force, and heat, and connecting them by common relations” (No. 2702, 1850). To this end Faraday tried to detect the appearance of currents in a wire coil falling from a great height, or in a long coil within which a foreign body falls, etc.; however, all the effects he observed, as he himself proved, were due only to secondary circumstances. And Faraday concludes his article with the following characteristic words: “For the present my experiments end here. Their results are negative. They do not shake my deep conviction of the existence of a connection between gravitation and electricity, although they do not provide proof of the existence of such a connection” (No. 2717).

Fig. 2. Faraday at work in the Royal Institution laboratory.

This task of finding a connection between gravitation and elec-

tricity, posed by Faraday, and remains topical even now; this is evidenced at least by the fact that Einstein devoted the last ten years almost entirely to attempts to solve it, to attempts to establish a unified field theory.

The period in the development of physics characterized by the development of ideas about the unity of the forces of nature was crowned by the establishment of the law of conservation of energy by Robert Mayer, Joule, and Helmholtz in 1842–1847. It is very interesting that Faraday, quite independently of these scientists and even before they published their discoveries, was fully clearly aware of, and in fact made use in his reasoning and argumentation, if not of the very law of conservation of energy in its exact quantitative formulation, then at any rate of one of its most essential parts—the principle of the impossibility of perpetuum mobile and the mutual convertibility of the forces of nature in equivalent ratios. Thus, in 1837 he wrote in his working diary: “It is necessary to compare the quantities of material forces, i.e., the forces of electricity, gravitation, chemical affinity, cohesion, etc., and, where possible, to give expressions for their equivalents in one form or another.”*

In 1839 he wrote a work on the theory of galvanic cells. At that time one of the central places in the outlook of physicists and chemists was occupied by the many-years-long, embittered dispute between the supporters of the contact and the chemical theories of galvanism: the former maintained that the cause of the current in a galvanic circuit is the very fact of contact between different conductors, while the latter saw the source of the current in the chemical reactions taking place in the circuit. In the work of 1839 Faraday, who was a supporter of the chemical theory, after masterfully setting forth the experimental investigation of the question that he had carried out, gives, in conclusion, the following consideration as the decisive argument: “The contact theory assumes that force can arise from nothing, that a current can be produced without any

* Quoted from Ostwald’s book Great Men, p. 128.

changes in the matter acted upon, or without expenditure of the producing force; moreover, this current would act by continuously overcoming a constant resistance. This would in fact be the creation of force, and in this this current would differ from every other force. We know many processes by virtue of which the form of force is so changed that there occurs a visible transformation of one force into another. Thus we can transform chemical force into an electric current, and an electric current into chemical force. The splendid experiments of Seebeck and Peltier prove the convertibility of heat into electricity, and the experiments of Oersted and mine—the convertibility of electricity into magnetism. But there is never any creation of force, any arising of force without a corresponding expenditure of that which feeds this force”*.

Thus Faraday was indeed a herald of the law of conservation of energy. It is remarkable, however, that Faraday, to the end of his life, was never able to arrive at a correct understanding of this law, was unable to grasp the difference between the concept of force and the concept of energy or work. For the law of conservation of energy by no means reduces to the simple assertion that nothing arises out of nothing. Among the great variety of physical quantities, properties, and qualities it is necessary to find precisely that quantity, that universal measure of physical phenomena, which remains quantitatively constant in all processes. The principal difficulty standing in the way of solving this problem, already long ripe in Faraday’s time, as also in the way of solving a whole series of other fundamental problems of physics in other epochs of its development, lay in operating with physical concepts that seemed simple, but in reality were insufficiently clearly outlined and defined. The most difficult step toward establishing the special principle of relativity was the analysis of the concept of simultaneity, and toward establishing the principles of quantum mechanics—the analysis of the concept of measurement. Helmholtz’s famous memoir is entitled “On the Conservation of Force”;

* “Exp. Res.,” No. 2071; cited according to the translation in Ostwald’s book.

under the word force was then understood both what we now call force and what we now call work. A correct analysis of this complex concept is one of the most important achievements of the founders of the law of conservation of energy.

This analysis, however, remained incomprehensible to Faraday. Here is what he says, for example, in one article of 1857 on the question of the force of gravity: “This [ordinary] view of the force of gravity seems to me to contradict the principle of the conservation of force; this contradiction is represented by the following part of the definition of the force of gravity: [the force of gravity] varies inversely as the square of the distance... Let us take, in empty space, two masses \(A\) and \(B\), between which there acts, from one to the other, a force by virtue of which they mutually attract each other, and let this force... vary inversely as the square of the distance... Suppose that, when the distance between the masses is equal to 10 units of length, the force is equal to 1; then, at a distance of 1, i.e. 10 times smaller, the force will be equal to 100. Let us suppose that between the masses there is an elastic spring, serving as a measure of the force acting between them; then in the second case the tension experienced by the spring will be 100 times greater than in the first case. But how did this enormous increase of force come about? If we say that it is a peculiar feature of this force, and content ourselves with such an answer, then, it seems to me, we shall be presupposing the creation of force, creation in such an enormous quantity and, moreover, owing to so simple and so insignificant a change of state that even the most undisciplined mind would not consider it a sufficient cause... We would abolish the highest law of the physical sciences—the law of the conservation of force. Let us suppose now that the masses \(A\) and \(B\) are again removed to their former distance from each other; then the attraction will amount to only one-hundredth of the former value, according to the law that the force of attraction is inversely proportional to the square of the distance. We would again obtain an astonishing result, since this would mean the annihilation of force, a phenomenon always accompanying creation …”

Fig. 3. A page from Faraday’s diary.

of a new force, and occurs only because it gives rise to this new force.”

Here is what Ostwald says on this subject: “At the present time it seems astonishing to us that such a clear and profound mind as Faraday’s could not resolve the misunderstanding arising from the fact that the word ‘force’ was then being given different meanings. Faraday even cites Helmholtz’s monograph on the conservation of force . . . Before his eyes he undoubtedly already had the solution to this riddle, but he did not see it.

It is not easy to find an explanation for this remarkable phenomenon. Senile self-doubt is entirely ruled out by Faraday’s open and modest character. In a state of mental overwork, in which he subsequently found himself almost continuously, independent work of thought is still possible in the rare hours following a prolonged rest; such work will even bring pleasant sensations; but the mind in such a state resists the assimilation of others’ thoughts much more strongly: to every such attempt it reacts with passive resistance. Therefore we may suppose that, since Faraday himself was no longer able to clarify the error arising from the use of one and the same word in different meanings, an error that concealed the essence from him, he could no longer be directed onto the true path by anyone at all, since his mind resisted the perception of another’s explanation. And in this remarkable case there again appears before us, in its harshest form, the limitation of human capacities even among our greatest representatives, to whom Faraday undoubtedly belongs.”

Let us now turn to the consideration of the evolution of Faraday’s views on the nature of electromagnetic forces. Whereas on the question of the unity of the forces of nature Faraday was only one of the best exponents of the ideas prevailing in his time, on the question of the nature of electromagnetic forces he appeared as a bold innovator. Faraday’s brilliant experimental discoveries immediately found universal recognition; his theoretical views, however, on the aforementioned

question, which served him as a reliable guiding thread in these discoveries, remained essentially incomprehensible to his contemporaries; they treated them as strange and vague speculations, at times almost contemptuously, as the eccentricities of a man who had failed to master the true theory of action at a distance.* It took the creative work of a kindred genius, Maxwell, who clothed Faraday’s ideas in precise mathematical form, to make the content of these ideas accessible to a wide circle of scientists.

At the beginning of the nineteenth century, Newton’s law of universal gravitation was regarded as the model for all laws of force. Coulomb’s laws had the same form. And it is no accident that Ampère, immediately after the discovery of the mechanical interaction of currents, cast the laws of this interaction in the classical form of laws of action at a distance, inversely proportional to the square of that distance and directed along the straight line connecting the interacting bodies. True, in doing so Ampère, unlike the classical model, had to take as the interacting elements not points but segments of lines (current elements). And how much labor and ingenuity Franz Neumann, Weber, and others later expended in order to cast the law of induction of currents discovered by Faraday into the same form of a law of action at a distance!

To Faraday, however, the very hypothesis of action at a distance seemed incomprehensible and unsatisfactory. To the analytical mind of Ampère or Weber, the reduction of the laws of electromagnetism to the classical forms of elementary interactions afforded satisfaction; but to Faraday’s synthetic mind, which thought in vivid geometrical images and was always alien to mathematical

* Here, for example, is a quotation from a letter by so eminent a scientist as Airy, dated 1855 (quoted from the book by Bence Jones, vol. II, p. 353): “I declare that I can with difficulty conceive that anyone who practically and quantitatively knows the agreement between observations and calculations based on the law of action at a distance could for even a single moment hesitate in choosing between this simple and exact action, on the one hand, and something so obscure and indefinite as lines of force—on the other.”

of analysis, this information, apart from all considerations of principle, could not but appear artificial. The essential properties of phenomena, as they are given to us in experience, can be described naturally and directly with the aid of the concept of magnetic lines of force, “by which I mean lines of magnetic force, ... as they may be traced out by iron filings, or lines to which a very small magnetic needle becomes tangent.”* And Faraday, in his very first paper on the induction of currents, formulates the law of this induction with the aid of the notion of the conductor’s cutting these magnetic lines. But if the cutting of lines in a medium, say between the poles of a magnet, excites currents, does this not mean that the magnetic lines in the medium are not merely a mental image, but also have a real existence?

In Faraday’s paper of 1833 there is a well-known passage where the electric current is defined as an “axis of power, having contrary forces, exactly equal in amount, but opposite in direction.”** Nineteen years later we find the following explanation: the meaning of this definition is “perfectly exact and means that the forces are contrary not because they have opposite directions, but because they are contrary in their nature; turn one of the forces [through 180°], and it will not thereby become like the first” (No. 3265). This example may serve to illustrate how difficult it sometimes really is to understand Faraday’s thought; and in a speech devoted to his memory, Helmholtz recalls how often he sat, hopelessly trying to discover the meaning of such statements by Faraday.

For us, however, what is now most essential is that the definition of current as an axis of power corresponds completely to Faraday’s later views on the nature of forces. A force does not act directly between two distant points; in every action of a force all the intervening

* “Exp. Res.,” No. 114, 1831.

** “Exp. Res.,” No. 517.

precise space between these points. The axis of action is essentially the same as what was later designated by the term line of force.*

In the aforementioned article of 1833, Faraday criticizes the theories of Grotthuss, Davy, and de la Rive, according to which the substances liberated during electrolysis at the electrodes are attracted to the electrodes from the solution by forces inversely proportional to the square of the distance from the electrodes. For, says Faraday, according to this assertion the intensity of electrolytic decomposition and the strength of the current would have had to diminish with distance from the electrodes, which, however, contradicts the results of a series of experiments specially arranged by him.**

Thus denying the determining role of the electrodes, Faraday comes to the conclusion that the current in the electrolyte is conditioned not by external forces of attraction of the electrodes, but by internal forces of interaction of adjacent particles of the electrolyte; moreover, in the presence of a current the forces of ordinary chemical affinity are weakened in one direction and strengthened in the opposite direction; therefore the constituent parts of the molecules pass from molecule to molecule until they reach the electrode (Nos. 518–519, 524).

Thus the conception of lines of force and of the role of the interaction of adjacent particles of the medium is expressed with complete clarity already in the first memoirs of the series “Experimental Researches.”

The fruitfulness of these conceptions was strikingly confirmed in 1837 by the discovery of the polarization of dielectrics, the dielectric constant, the dependence of the capacitance of a condenser on the intervening medium, and so on. Like most of Faraday’s discoveries, these discoveries were by no means

* Cf. Rosenberger, vol. II, p. 284.

** The most convincing of these experiments, for some reason, is more rarely mentioned in the literature than all the others. Faraday showed that, in the case of an electrolyte of constant cross-section situated between two flat parallel electrodes of the same cross-section, the fall of potential per unit length (we use present-day terminology) does not depend on the distance from the electrodes (“Exp. Res.”, No. 502).

were not accidental, but were the result of persistent searches in a quite definite direction, and Faraday himself, in the first paragraphs of his memoir of 1837, establishes the connection of these discoveries with the views he had developed concerning the nature of current. Electrolytes in the solid state (for example, ice), as Faraday discovered in 1833, do not conduct current, but they do not hinder the electrostatic interaction (in Faraday’s terminology—induction) of bodies separated by them. Consequently, induction is the primary stage, and electrolytic decomposition (after the melting of the electrolyte) is the secondary one. And since the current in the electrolyte is reduced to the interaction of adjacent particles, “I began to suspect that ordinary induction in all cases is an action of adjacent particles, and that electrical action at a distance (i.e. ordinary inductive action) always takes place only through the mediation of an intervening substance” (No. 1164).

In the note to this paragraph Faraday observes that the term “adjacent” is “not quite exact, since the particles do not touch one another.... By adjacent particles I mean particles nearest to one another.” And a little further on he examines in more detail the question of the transmission of forces through an absolute vacuum. “Let us suppose that a positively charged particle may be situated at the center of a void one inch in diameter. According to my present views, nothing prevents this particle from acting at a distance of half an inch upon all the particles forming the inner surface of the bounding sphere, with forces obeying the known inverse-square law of distance. But suppose that this sphere of one inch were filled with an insulating substance; then, according to my notions, the electrified particle would not act directly upon the remote particles, but only upon those immediately adjoining it (those in immediate association with it), expending all its force on their polarization”*. Faraday’s further explanations may be briefly re—

* “Exp. Res.”, No. 1616.

are given thus: all the lines of force issuing from the central electrified particle terminate on the adjacent particles, which are thereby polarized, so that from their outward-facing portions there in turn issue lines of force terminating on the particles of the next layer, and so on. As a result, particles one inch away, which in the case of a vacuum would be subject to the direct action of the central particle, are subject to an indirect action of the same magnitude and direction, transmitted by the intermediate particles of the medium.

Thus Faraday’s theory, at least at the stage under consideration, was not a consistent theory of action at a distance, but rather a theory of “limited action at a distance” between adjacent particles. Later, however, the conception of lines of force penetrating the vacuum acquired ever greater definiteness and tangibility. Already in the aforementioned memoir of 1837 there is a remarkable discussion of the existence of lateral pressure between adjacent lines of force. Even now, in the light of a century of development and popularization of Faraday’s ideas, it is extremely difficult to understand the course of Faraday’s thought, who, after setting forth the experimental proofs of the curvature of the lines of force when conductors are introduced into the field, comes to the conclusion: “Nothing can prove this better than the curvature of the lines or paths of inductive action ..., as also, so to speak, the lateral pressure of these lines upon one another”. The full significance of this difficult-to-understand train of thought becomes clear only in the light of the subsequent researches of Maxwell, who, by means of complex mathematical analysis, showed, as is well known, that the system of mechanical forces in an electric field can be completely reduced to tensions along the lines of force and pressures perpendicular to them. The quite exceptional depth of Faraday’s intuition apparently enabled him directly* to discern these relations in the results of the very first series of experiments!

Having proved the influence of the medium on electrical actions, pro—

* “Exp. Res.,” No. 1224; see also Nos. 1297 and 1304.

having become convinced of the correctness and fruitfulness of his ideas, Faraday, already in the following year, 1838, carried out a series of experiments in order to determine whether the medium also exerts an influence on magnetic actions, and whether magnetism is not transmitted at a distance through the action of intermediate particles*.

The first experiments yielded negative results, and a series of failures continued to pursue Faraday for a long time. This period coincided, meanwhile, with a second, very acute period of decline in his activity and of complete exhaustion, caused by the extreme strain of creative work. In the six years 1839–1844 Faraday published only four memoirs—no more than in the single year 1838—and these were of comparatively secondary significance. For four years, with the exception of one series, he carried out no experiments on electricity. He had to seek treatment by taking rest in Switzerland and at the seaside; he had quite consciously and severely to reduce or entirely stop lectures, meetings, consultations, to decline invitations to society, to dinners, etc. In February 1843 he writes to Matteucci: “Yesterday I received your letter and was touched by your friendly expression of interest in a man who feels that his purpose in this world is already behind him… My health and spirits are, to be sure, good, but my memory has vanished.” A year and a half later he writes in another letter: “In my thoughts there wander many beautiful discoveries which I formerly hoped, and still now desire, to realize; but when I turn to work, I lose all hope, for I see how slowly it advances for lack of time and strength; I feel that this work may perhaps be bringing into being the last of all those ideas which I could put into practice. I do not say that my mind refuses to work; I say only that the psychophysical functions coordinating the work of mind and body are weakening, especially memory. Hence—a considerable reduction in the amount of work I produce. For this reason I have had to change greatly the character of my life and work: I have ceased intercourse with colleagues in special—

* “Exp. Res.”, No. 1662, 1710.

ness, limited the number of his investigations, which, perhaps, might have led to discoveries. I often have to turn to my family doctor with complaints of headache, dizziness, and so on, and he often orders me to abandon troubling thoughts and mental work and go to the seaside, so as to do nothing.”*

Only in 1845, at the age of 54, did Faraday recover enough to be able to take up work again. This year 1845 at once brought two fundamental discoveries: the discovery of the rotation of the plane of polarization of light by a magnetic field, which we have already mentioned, and the discovery of the universality of the magnetic properties of matter—the phenomena of diamagnetism. The title of the first memoir is characteristic: “On the Magnetization of Light and the Illumination of Magnetic Lines of Force.” The lines of force, of which Faraday in 1837 had spoken quite definitely: “These lines are imaginary” (No. 1304), had by this time acquired in his conception a much greater concreteness. In a note to the memoir just mentioned, Faraday observes that its title had been incorrectly interpreted by some as meaning that Faraday wished to say that he had made the lines of force shine. “This was not my intention. I wished to express that a line of magnetic force was illuminated in the same way that the earth is illuminated by the sun, or that a spider’s web is illuminated by an astronomer’s lamp. Using a ray of light, . . . we can, by the optical action of the ray on the eye, see the path of the magnetic lines just as we can see the path [position] of a glass thread or of any other transparent substance which becomes visible in the light” (No. 2146). And to Faraday’s mental vision these lines did indeed appear as a complex web, binding the individual particles of matter into a single all-embracing system.

The discovery of diamagnetism that followed in the same year solved the problem posed in 1838—to demonstrate the influence of the medium on magnetic phenomena. Faraday, however, believed that in the question of the transmission of forces at a distance by particles of intermediate

* Quoted from Ostwald, p. 116.

the intervening medium, the discoveries and phenomena investigated by him in diamagnets do not possess that degree of evidential force with respect to magnetic forces which, in his opinion, phenomena in electrolytes and dielectrics possess with respect to electric forces.

We are unable to follow with the same detail the further development of Faraday’s ideas, just as we are unable to touch upon his investigations in the field of electric discharges in gases (“Faraday’s space”), electrification and the liquefaction of vapors and gases, terrestrial magnetism, magnetocrystalline effects, and so on. In conclusion we shall touch only upon Faraday’s views on the question of the physical reality of lines of force.

Created by Faraday in opposition to the prevailing theories of action at a distance, the conception of lines of force fully justified itself in practice: it proved a faithful guide for Faraday on the path of numerous brilliant discoveries; with the aid of the same conceptions he succeeded in formulating all the known and newly discovered laws of electromagnetism. Various dielectrics, as well as various magnetic substances, differ in their permeability to lines of force. If a more permeable body is placed in a less permeable medium, a larger number of lines of force will choose a path through that body, which in turn will bring about the appearance of an attraction tending to move the body into the region of greater density of lines of force. On the surface of an isolated charged sphere the ends of the lines of force are distributed uniformly, so that the forces of attraction exerted by these lines mutually compensate one another. But if another charged body is brought near this sphere, then the lines of force will be redistributed in a definite way in space, and their ends—on the surface of the sphere; and the resultant force of attraction of these lines, experienced by the surface of the sphere, will become different from zero. When the dimensions of the charged bodies are large in comparison with their separation, this resultant proves to be inversely proportional to the square of the distance.

Against the background of these successes it appears entirely natural—

...natural, that Faraday comes to the following conclusion:

“I can only say that in no part of space, whether it be (to use the usual phraseology) devoid of matter or filled with it, can I represent to myself anything except forces and the lines along which they act.”

This phrase is taken from the article “Thoughts on Ray-Vibrations” in Phil. Mag. for 1846, which Faraday did not include in the series of Experimental Researches because of its “speculative character.” In it he expresses the supposition that the most elementary particles of matter may perhaps be nothing but a force field—electric, magnetic, and gravitational—surrounding a point center. According to this view, essentially coinciding with the views of Boscovich, the atom has no definite size, but rather must be considered wholly permeable and extending throughout all space, and the molecules of chemical compounds must consist not of a group of mutually touching atoms, but of “mutually interpenetrating spheres of action, the centers of which may even coincide.” Finally, light and radiant heat may be transverse vibrations propagated along lines of force filling all space. And Faraday proposes, as we have already mentioned, thus to eliminate the concept of the ether (dismiss the aether*) or, more precisely, to replace it with the totality of lines of force connecting the centers of forces with one another.

Faraday, however, always distinguished hypotheses from facts with the highest degree of scrupulousness, and always persistently emphasized that the possibility of a correct and exact description of electromagnetic phenomena by means of the conception of lines of force still in no way settles the question of the true nature of these phenomena. Naturally inclining to the view that lines of force possess physical reality, Faraday in the late 1840s and early 1850s devoted several articles to this question, each time adding the reservation that these articles were “of a highly hypothetical and speculative character.”

* Quoted from Bence Jones, l. c., vol. II, p. 178.

Three main arguments are adduced by Faraday in defense of the physical reality of electric and magnetic lines of force, whereas he regards gravitation as acting at a distance:

1. The polarity of electricity and magnetism, in contrast to gravitation acting at a distance, which possesses no polarity (for negative masses do not exist). In the case of polar forces, “one force finds or excites near itself an opposite force and therefore cannot propagate into the distance”*. And further: “Unlike gravitation, the [electric] force is limited [in magnitude]. A given electric particle cannot act upon a second, third, and fourth particle in the same way as upon the first; in order to act upon the subsequent ones, its force must in the corresponding part be subtracted from the preceding particles” (No. 3248). The meaning of this reasoning (cf. p. 22) evidently amounts to the assertion that from each charge there issues a perfectly definite number of lines of force, the ends of which are merely redistributed among neighboring charges of the opposite sign. It is, however, difficult for us to discern in this respect any distinction between electromagnetic forces and gravitation.

2. Unlike gravitation, electric and magnetic interactions depend on the intervening medium.

3. Finally, electric and magnetic lines of force are curved, whereas gravitation acts rectilinearly: “I cannot conceive of curved lines of force outside the conditions of physical existence [of them] in the intervening space”** (No. 3258, see also No. 3254).

None of these arguments is now decisive for us. We know that, in the domain of static and quasi-stationary electromagnetic phenomena, to the study of which Faraday in essence confined himself, the theory of lines of force, both in its original and in its modern form (field theory), and the theory of action at a distance

* Cf. Whittaker, p. 217.
** Quoted from Rosenberger, p. 296.

completely equivalent: each of them is capable of describing the entire aggregate of phenomena quite correctly, differing only in the concentration of attention, in the bringing to the fore of one definite group of their manifold properties. In particular, the influence of the medium is explained by modern electron theory in a way which, in essence, corresponds fully to the pure Coulomb theory of action at a distance; moreover, it makes use of precisely those ideas of the polarization of dielectrics and the magnetization of magnetic bodies which Faraday himself often employed.

The sole decisive argument in favor of the physical reality of the field is for us the finite velocity of propagation of electromagnetic fields in conjunction with the law of conservation of energy. For from these two laws it follows that the electromagnetic field, even in the absence of ponderable matter, may be the bearer of electromagnetic energy. Faraday himself was fully aware of the decisive significance of the time element in the question of the physical reality of lines of force, but he did not, of course, possess the corresponding experimental data.

Yet even in the domain of stationary electromagnetic phenomena Faraday’s conceptions proved highly fruitful, for, while distinguished by extraordinary visual clarity, they focused attention precisely on those aspects of phenomena and made it possible to grasp at a glance precisely those relations which, when theories of action at a distance were used, remained in the shadows and required a considerably more complex analysis.

Modern electron theory is, in essence, a distinctive synthesis of Faraday’s views and the theories of action at a distance. To the theories of action at a distance correspond such features of modern views as: the cardinal role assigned to electric charges, the conception of their substantiality, the modern electron theory of the complex phenomena occurring in conductors, dielectrics, and magnetic bodies, and, finally, the reduction of electromagnetic phenomena to the “retarded action at a distance” of charges (retarded potentials). On the other hand, the pos—

Faraday’s views correspond to the recognition of the physical reality of the electromagnetic field as the bearer of electromagnetic energy, and to the very idea of action by contact, according to which all phenomena at a given space-time point are completely determined by the states of the space-time points adjacent to it.*

Of course, the very idea of action by contact has undergone a substantial evolution over the past century. The conception of lines of force will always retain its significance as making it possible to understand, in an extremely simple and visual way, a whole domain of rather complex phenomena. However, we now know that the area of its applicability is limited, that in other domains of electromagnetic phenomena, and above all in rapidly varying fields, it only obscures the essence of the matter, or refuses to serve at all and leads to contradictions. But it was precisely from the conception of lines of force that the concept of the field crystallized, a concept of such fundamental importance for all modern physics.

The modern concept of the field fully corresponds to the essence of Faraday’s views. And the historian of physics Rosenberger is quite right in his assertion that Faraday “in the end arrived at the quite radical conception of the materiality of continuous space.”** Here the question is by no means one of mechanistic theories of the ether, of which Faraday was never a supporter. The complete untenability of the attempts, so characteristic of nineteenth-century physics, to reduce electromagnetic phenomena to the mechanics of a hypothetical medium—the ether, with complete definiteness—became clear even before the theory of relativity eliminated every possibility of a return

* Throughout this article we consistently use exclusively classical, i.e., pre-quantum, conceptions. It is known that the attention of quantum theory is now focused precisely on the problem of the field (electrodynamics), and that the solution of this problem, possible only on the basis of a physical, and not merely formal, synthesis of quantum theory and the theory of relativity, will undoubtedly be connected with a radical reconstruction of a number of our basic physical views.

** Rosenberger, cited work, vol. II, p. 305.

to these aspirations. The so often unfortunate confusion of the question of the materiality of space, or of the ether, with mechanistic theories of the ether is based to a considerable degree on a confusion of the two senses in which the word “matter” is used.

The physicist usually uses this word in a narrow sense, corresponding essentially to the concept of ponderable bodies and the concept of substance. In this sense of the word, light, for example (although it does in fact possess weight), or the electromagnetic field, are not matter at all.* In the broader, philosophical sense of the word, however, matter is any objective physical reality existing in time and space. And in this sense not only light, but also the ether—the bearer of the physical properties of space—is undoubtedly material. For physical space does not at all represent merely an “empty” extension into which material bodies are, as it were, inserted. No, space possesses complex physical properties—it is the bearer of electromagnetic and gravitational fields, the bearer of energy. The states and properties of space, up to and including geometrical properties (the general theory of relativity!), are determined by the bodies situated in it and in turn act upon these bodies.**

And this conception of space as a living physical reality, in continuous interaction with all the bodies situated in it, has one of its principal sources, undoubtedly, in Michael Faraday.

* From the modern point of view, the distinctive characteristic of matter in this narrow sense of the word is not the weight or mass possessed by all forms of energy, but 1) the presence of an electric charge (electron, proton, atom, molecule, etc.) and 2) the presence of a nonzero rest mass (Ruhmasse) in the sense of the theory of relativity.

** However, the greatest mistake is the conception of the ether as a continuous fluid or as an aggregate of the tiniest atoms, as well as, in general, any conception of spatial displacements of the “elements” of the ether.

Literature

1. M. Faraday, Experimental Researches in Electricity. 3 vols. London, 1839–1855. There is a German translation in the series “Ostwald’s Klassiker.”

2. M. Faraday, Experimental Researches in Chemistry and Physics. London, 1859.

3. Bence Jones, Life and Letters of Faraday. 2 vols. London, 1870. The most comprehensive biography of Faraday, containing, in addition to Faraday’s correspondence, excerpts from his diaries, notebooks, speeches, and lectures.

4. E. T. Whittaker, History of the Theories of Aether and Electricity. Dublin, 1910. An excellent book, chapter 6 of which is devoted to Faraday’s views.

5. F. Rosenberger, Geschichte der Physik. 3 vols. Braunschweig, 1887–1890 (there is a Russian translation). One of the best histories of physics. About 40 pages in vol. III are devoted directly to Faraday.

6. W. Ostwald, Great Men. Translated by Kvasha. St. Petersburg, 1910. The fourth lecture contains a very interesting analysis of the psychophysiological features of Faraday’s talent and significance.

7. H. H. Helmholtz, Die neuere Entwicklung von Faraday’s Ideen über Elektrizität. A speech delivered in 1881 and reprinted in Naturwiss., 19, 793, 1931. Special attention is given to the theory of electrolytes and the galvanic battery.

In addition, in connection with the celebration of Faraday’s jubilee, a large number of articles devoted to him appeared in a number of journals (Nature (Engl.), Reviews of Modern Physics, etc.).