Chapter XII: The National Research Council 349 (9)

The summer vacation was on and I decided to take Faraday’s “Electrical Researches” to Scotland, the land of Maxwell. In the preface to his great--and to me, at that time, enigmatic--electrical treatise Maxwell modestly had stated that he was an interpreter, only, of Faraday. But I was delighted when I heard Tyndall’s suggestion that Faraday would help me to interpret Maxwell. Perhaps, thought I, the invigorating air of Maxwell’s native Scotland would help me to catch some of the ideas which Maxwell had caught when he was reading Faraday. I selected what I thought would be a quiet and secluded spot, the island of Arran. It belonged to the Duke of Hamilton, and I was told that his grace had imposed so many restrictions upon his tenants that the island had become an ideal spot for those who sought seclusion. I found there a neat little inn at Corrie. It was surrounded by several tiny cottages for summer visitors who took their meals at the inn. It was popular with people from Glasgow, Greenock, and Paisley. Every one of the visiting families was blessed with numerous daughters. They were very athletic and played tennis from early morning till late in the afternoon, interrupted now and then by swimming contests in the frigid waters of the Firth of Clyde. In the evening there was lively dancing--not easy-going waltzing, but the real fling and reel of the strenuous Highland type. “What a sturdy race this is,” I said to myself, as I watched the dancers working themselves up into a frenzy of rhythmic movements, one hand resting upon the hip, the other raised high up in the air, while their joyful limbs were pumping up and down in perfect rhythm as if they were busy pulling up from mother earth all the earthly joys stored up there for mortal man. The whole scene was particularly thrilling to me when a piper came along and furnished the music. The bagpipes reminded me of my native Idvor, and made me feel at home in bonny Scotland before I had been much over a week in Arran. The Scotch and the Serbs have many things in common, and I always believed that somewhere back in the history of Iran they must have belonged to the same tribe. I am told that at the Macedonian front the Scotch and the Serbian soldiers got along beautifully, as if they had known each other from time immemorial, and they had little use for the other races assembled there. I got along at Corrie as if I had known the Scotch all my life. But that had its disadvantages also. I came to Corrie looking for seclusion where, undisturbed, I could communicate with Faraday. But the lively lassies from Glasgow, Greenock, and Paisley, the tennis and the swimming contests, the fascinating sound of the bagpipes accompanying the stirring Highland dances--all these things whispered into my ear: “Faraday can wait, but your friends here cannot.” Then I remembered a passage in one of Maxwell’s letters, given in Campbell’s life of Maxwell, which said: “Well, work is good and reading is good, but friends are better.” What a splendid excuse for joining the lassies and the lads at Corrie and revelling in the healthful pursuits of their youthful exuberance! Besides, said I to myself, have I not accomplished enough during my eighteen months’ drilling under Routh, Maxwell, La Grange, Rayleigh, Stokes, and Tyndall to deserve a complete change of mental and physical activity? When a person looks for an excuse to do what he or she likes to do a splendid excuse can always be found, and so I bade a temporary farewell to Faraday’s “Electrical Researches,” and joined the playful activities of my Corrie friends, challenging them to go the limit. In tennis and swimming I held my own, but the Highland reels floored me every time, until Madge, one of the sturdy lassies from Greenock, by persistent private instruction finally succeeded in initiating me into the mysteries of the Highland rhythm. Glen Sannox, near Corrie, with its rich bed of heather, watched me often by the hour making many futile efforts to catch this rhythm and make my limbs obey it. Nobody else watched these efforts in lonely Glen Sannox excepting Madge, and she, I told her, had more fun than a Bosnian gypsy training his bear. I can still hear the slopes of Glen Sannox echoing the clear notes of her ringing laughter, whenever I made an awkward and clumsy movement in my persistent efforts to master the Highland fling or reel. She could not help it, and I did not mind it, because I had made up my mind to do the trick or die. Finally I did it, not very well, but well enough for a fellow who was not a Scotchman, and Madge presented me with my portrait in pencil, which she drew during the intermissions between my efforts to master the art of the Highland dances. That was my reward and it was a very good one; she was a most promising young artist who had won several prizes in the Greenock art school. The memory of this experience always recalled to my mind the thoughts which went through my head at that time--the thoughts, namely, that Scotch originality, individuality, and sturdiness are hard to follow, not only when a foreigner meets these wonderful qualities in the mental activity of a Scot, like the mental activity of a Maxwell, but also in physical activity like that displayed in the national dances of Scotland. One does not appreciate fully the wonderful qualities of the Scot until he tries to master the theory and the practice of the Highland fling or reel. Maxwell’s electrical theory, I thought, might be just as different from other electrical theories as the Highland dances are different from the dances of other nations. I found out later that my guess was not very far from the truth.

Several years ago I was driving through the streets of London, visiting England again after an absence of many years. Suddenly I saw a crowd watching a Scotch dancer. The dancer was a young woman in Highland costume, and she was dancing the sword dance exquisitely; her husband was playing the bagpipes, marching up and down with all the swagger of the Scotch Highlander. I stopped my cab, got out, and watched. The memories of Corrie and Oban and of the gathering of the clans there which I witnessed while at Arran came back, and I was thrilled. Presently the dancer reached me in her tour soliciting voluntary contributions. I threw a sovereign into her plate and she looked surprised and asked me whether I had not made a mistake. “Yes,” said I, “I did make a mistake when I went out with only one sovereign in my pocket. If I had two you should have them both.” “Are you a Scotchman, sir?” she asked jokingly, and when I said “No” she smiled and said: “I did not think you were.” She knew that there was a fundamental difference between a Scot and a Serb.

After I had been at Corrie for about a month a letter arrived from my mother, written by my oldest sister, telling me how happy she was that I had decided to spend my summer in Scotland for the purpose of meditating over the life and the work of one of the greatest “saints of science.” I meant Faraday when I wrote to her. She also told me that Idvor was fearfully dusty on account of a long-continued drought, and that the crops were poor and the vintage prospects even poorer, and that Idvor was not a very cheerful place during that summer for anybody who wished to meditate free from complaints of grumbling neighbors. “Berlin, I am told, is much nearer to Idvor and when you are there you can always run down to Idvor, much more easily than you can now,” she said, closing her letter, in which logic and motherly love vied with each other to furnish her with a consolation for my absence from Idvor during that summer.

My mother’s letter made me feel guilty and it called for a reconsideration of my first resolution, adopted a month earlier, which authorized me to bid a temporary farewell to Faraday’s “Electrical Researches”; and I passed another resolution rescinding my first. But the question arose, how to carry it into effect. The answer was obvious: bid good-by to Corrie. My friends, however, suggested a less obvious but certainly a much more agreeable answer. “Go up and live in the Macmillan homestead, and read your Faraday there in the morning and come down to Corrie for dinner, late in the afternoon,” suggested Madge, and the suggestion was adopted without a dissenting voice on the part of my young friends.

The Macmillan homestead was a very humble old cottage located half-way between Corrie and the top of Goat Fell Mountain, the highest point on the island of Arran. An old crofter and his wife lived there, leading one of the most frugal existences that I had ever seen anywhere. They were willing to furnish me with lodging and simple breakfast, consisting of tea and oatmeal porridge with some bread covered with a thin layer of American lard. I did not object; I was prepared to take up low living and high thinking for the love of Michael Faraday. Communion with Faraday from early morning until four in the afternoon, and after that any play that came along, with plenty of dancing in the evening, was a splendid combination. Practically one solid meal a day, my dinner at the Corrie inn, supplied the fuel for all this activity, and it did it satisfactorily. How could I complain? The man whose wonderful scientific discoveries I was absorbing each day started life as a bookbinder’s apprentice, and the founder of the great Macmillan publishing-house was born and passed his boyhood days in the humble cottage where I was lodging. I was sure that in their youth they never had more than one solid meal a day and they prospered. My rapid absorption and digestion of the mental food which Faraday offered I attributed to my avoidance of superfluous physical food, but I must confess that I was quite hungry when dinner was served at the Corrie inn, and I enjoyed it immensely.

I never understood the full meaning of low living and high thinking as well as I did while I was a lodger at the Macmillan homestead. My thinking machinery, I thought, never worked better, and even my vision, always very good, seemed to be better than ever before. On exceptionally clear days I was sure that from the high elevation of the Macmillan cottage, on the slope of Goat Fell Mountain, I could see the beautiful Firth of Clyde as far as Greenock and Paisley, and at times even the gray and gloomy edifices of Glasgow seemed to loom up in the distance. I bragged about it, but my friends at Corrie met my bragging by informing me, jokingly, that any Scotchman can see much farther than that. One of them, a pupil of Sir William Thomson at the University of Glasgow, met my bragging by the epigrammatic question: “Can you see in Faraday as far as Maxwell, the Scotchman, saw?” I never bragged again about my vision while I was in Scotland. I was certain, however, that from the Macmillan homestead on the slopes of Goat Fell Mountain I obtained a deeper view into Faraday’s discoveries than I could have obtained in any other place. I seldom mention the names of Faraday and Maxwell without recalling to memory the beautiful island of Arran and the humble Macmillan homestead on Goat Fell Mountain.

VIII

STUDIES AT THE UNIVERSITY OF BERLIN

Every period in the history of mankind had its revelation in science. Some periods were most fortunate in this respect. The first half of the nineteenth century saw the great scientific revelation called the Principle of Conservation of Energy, and considered it its greatest glory. Our own American philosopher, Benjamin Thompson, of Woburn, Massachusetts, known in Europe as Count Rumford, was one of several early prophets in science who foresaw the advent of this great dynamical doctrine. Its importance to mankind cannot be overestimated. I am sure that many a scientific man of those days felt grateful to heaven for the blessing of having lived during the age when that great revelation was received by mankind. The scientific men of to-day are grateful for having lived during the second half of the nineteenth century, when the great electromagnetic theory was revealed to man. Its importance, likewise, cannot be overestimated. But there is a radical difference in the historical progress of these two nineteenth-century revelations in science. The existence of the first was intuitively foreseen and may be said to have existed in one form or another in the minds of many scientific men long before it received its final form of statement. Its formulator, Helmholtz, thought that he was not announcing anything new, but was only stating his own view of something that was already well known. After his announcement, in 1847, every scientific man accepted the revelation as an almost self-evident truth. The electromagnetic theory of light and of matter had a different history. It was born as a dim vision in the mind of a single man, Faraday, and nearly fifty years elapsed before it was formulated by Maxwell and experimentally demonstrated by Hertz. It was only then that the world began to understand that a great scientific revelation had appeared to man. To-day we know that new physical concepts requiring a new language for their expression had to be created in the minds of scientific men before the modern electromagnetic doctrine could be revealed to the world. The first glimpses of that revelation I caught on the slope of Goat Fell Mountain, and two years later I saw in Berlin what I believed to be a clear outline of its meaning.

When I look back to those days and consider how few were the physicists who had caught this meaning even twenty years after it was stated by Maxwell in 1865, I wonder whether it is possible to-day to convey that meaning to people who are not trained physicists. I think it is, and I believe that the attempt should be made, because the electromagnetic doctrine is to-day recognized to be the very foundation of all our knowledge of physical phenomena. I also think that one of the best methods of conveying that meaning is to describe my early attempts which failed to catch it.

MICHAEL FARADAY

Reproduced from Volume II of “The Scientific Papers of
James Clerk Maxwell,” edited by W. D. Niven. By
permission of the publishers, The University Press,
Cambridge]

Faraday’s discoveries in the electrical science during the first half of the nineteenth century attracted worldwide attention and admiration. I knew that much at Arran, and I also knew of the rapid growth of the practical applications of his discoveries, to telegraphy, to generation of electrical power for electrical lighting, electrical traction, and electrochemical work, and finally to telephonic transmission of speech. The world understood that all these wonderful things, which contributed so much to the comforts of mankind, came from those sources in the realm of abstract science which were opened up by Faraday’s discoveries. Scientific research began to assume a different aspect even in the eyes of the captains of industry who in those days showed lamentable indifference to science which did not promise immediate tangible returns. The advocates of scientific research, like Tyndall and his American and British friends, pointed with pride to Faraday’s work whenever a question arose concerning the practical value of research in the domain of the so-called abstract physical sciences. This helped very much to arouse in this country and in Great Britain a deeper interest in what Andrew White called “strength and hope for higher endeavor.”

But Tyndall’s and Maxwell’s descriptions of Faraday and of his work convinced me that Faraday’s exalted position among his contemporaries like Maxwell, Henry, Tyndall, and Barnard was due not so much to the immediate practical value of his electrical discoveries, great as that value certainly was, as it was to the clear vision with which he searched for and revealed new morsels of the _eternal truth_. It was clear to me even at that time that inventions are the handwork of mortal man and that, though at first they appeal to us, as they ought to, as wonderful creations of human ingenuity, their ultimate fate is to become more or less commonplace. The telegraph and the telephone, the dynamo and the motor, the light of the electrical arc and of the incandescent filament, had lost much of their awe-inspiring character even at the time when I was a student at Cambridge. Inventions grow old and are superseded by other inventions, and, being the creation of the constructive schemes of mortal man, are themselves mortal. But the laws which the stars and the planets obey and have always obeyed in their paths through the heavens are unchangeable; they never grow old, and therefore they are immortal; they are a part of the _eternal truth_. We do not know of any natural processes by which eternal things have been evolved. Their existence is the best philosophic proof that back of all this changeable visible world there is the unchangeable, the eternal divinity. Archimedes, Galileo, and Newton co-operated in the discovery of immutable laws, and thereby revealed to mortal man morsels of the _eternal truth_. Oerstedt, a hundred years ago, discovered a morsel of the eternal truth when he discovered the magnetic force which is produced by the motion of electricity. Discoveries of immortal things and of the immutable laws which direct the mission of their immortal existence are themselves immortal. Their discoverers are, and deserve to be, immortal. Tyndall and Maxwell were the first to show me that Faraday occupied a distinguished place among such immortals as Archimedes, Galileo, Newton, and Oerstedt.

The closing sentence of Maxwell’s biographical sketch of Faraday, in vol. VIII of _Nature_, referred to above, reads as follows:

We are probably ignorant even of the name of the science which will
develop out of the materials we are now collecting, when the great
philosopher next after Faraday makes his appearance.

To me these prophetic words indicated that Maxwell had something in his mind which was not explicitly expressed in Faraday’s discoveries, but which enabled Maxwell to speak like a prophet. The words of a prophet are not always easy to understand. I discovered later that, when the world with the aid of the Hertzian experiments had caught Maxwell’s meaning, then a new and wonderful epoch in the history of the physical sciences was inaugurated. Its end is not yet in sight. This inauguration I witnessed during my student days in Berlin. It is, I believe, of considerable interest to record here how the scientific world, as I saw it at that time, appeared to be preparing to receive the great revelation which was delivered to it on that historic inauguration day in 1887.

My communion with Faraday on the island of Arran began my own preparation for this inauguration day by developing gradually in my mind new physical concepts, which I discovered later to be fundamental physical concepts in the modern views of physics. Long before I had finished my reading of Faraday’s “Experimental Researches in Electricity,” I began to understand why Tyndall, referring to them, said: “Read them; their story is just as new and as stirring to-day as it was when these volumes were first printed. They will help you much to interpret Maxwell.” The same statement is true to-day, and therefore I proceed now, with much trepidation, to tell a part at least of that story as briefly as I can, in order to describe, even if it be quite inadequately, Faraday’s relation to the present great epoch of modern physics, the epoch of the electromagnetic view not only of _light_ but also of _matter_.

The gradual development of this view was due to the gradual development of new physical concepts which were born in Faraday’s mind and existed there as a poetical vision; but in Maxwell’s mind they appeared as physical quantities having definite quantitative relations to other well-known physical quantities, which a physicist can measure in his laboratory. In every creative physicist there is hidden a metaphysicist and a poet; but the physicist is less apt to persist in his occasional errors as metaphysicist and poet, because the creations of his speculative mind and of his poetical vision can be subjected to crucial experimental tests.

Faraday’s “Experimental Researches in Electricity,” published in three thick volumes, looked like very long reading. But my studies at Arran soon convinced me that no reading is long which continually stirs up the interest of the eager reader. Faraday was a pioneer in science, and the descriptions of his explorations read like tales from a new world of physical phenomena, full of poetical visions which his discoveries suggested to his imagination. It must be said, however, that in spite of his wonderful imagination and his free use of it, no investigator ever succeeded better than Faraday in drawing a sharp line of division between the new facts and principles which he had discovered and the visions which his imagination saw in the still unexplored background of his discoveries. For instance, his discovery that a perfectly definite and invariable quantity of electricity is, as we express it to-day, attached to every valency of an atom and molecule, expresses a physical law which his experiments revealed and which he illuminated with all the light of his brilliant intellect. But when this new and precious morsel of the eternal truth had been disclosed by his experiments, then Faraday the scientist stepped aside, and Faraday the poet disclosed his visions about the constitution of matter suggested by what I called at Arran the atomic distribution of electricity in material bodies.

A man who discovers one of the most remarkable facts in modern science, namely, that in every atom and molecule there are definite and equal quantities of positive and negative electricity, and that the forces between these electricities are by far the largest known forces which keep together the components of chemical structures, cannot, if he has the imagination of a discoverer, refrain from asking the question: “What is matter?” The reader of Faraday’s “Experimental Researches in Electricity” rejoices whenever Faraday, the poet and prophet, asks an apparently speculative question of this kind, because he knows that he will be thrilled by the poetical fancy which dictates Faraday’s answer. Faraday’s new facts and principles revealed by experiment are steeped in the honey of his fancy; they are rich food made delicious by the flavor of his poetical imagination, even when that flavor leaves the ordinary mortal guessing as to its exact meaning.

Two other questions Faraday often approached in these researches; they may be stated as follows: What is electricity? and, What is magnetism? He discovered that motion of magnetism produces electrical forces in a manner similar to that in which, according to Oerstedt’s discovery, motion of electricity produces magnetic forces. This remarkable reciprocal relation between electricity and magnetism stirs up the imagination, and makes it eager to look behind the curtain which separates the region of the revealed truth from that which is still unrevealed. It was undoubtedly this eagerness of the explorer which encouraged Faraday to approach the questions, What is electricity? and, What is magnetism? Faraday never gave a final answer to these questions, but his magnificent efforts to find this answer gave birth to new ideas which are the foundation of our modern electromagnetic view of physical forces. One of the great pleasures of my life has been the contemplation of the gradual unfolding of this new view; and if in the course of this simple narrative I succeed in describing some of its beauties, I shall consider that this narrative was not written in vain.

Since, as explicitly stated by Faraday, electricity and magnetism are known by the forces, only, which they exert, it was plain to him, as his books, “Experimental Researches in Electricity,” testify, that the first question which must be answered was the question: How are the forces between electrical charges and between magnetic charges transmitted through the intervening space--the same way as gravitational forces, or are they transmitted in a different way? In his unceasing efforts to answer this question Faraday made a radical and fundamental departure from the view of the natural philosophers of his time. He stood alone and devoted a very large part of his experimental work and of his philosophical thought to the justification of his position. He stood alone for a very long time, because he was formulating a radically new physical concept which the world knows now to be one of the most fundamental concepts of the electromagnetic science of to-day; and it was difficult for his contemporaries and for his students of forty years ago, including myself, to understand him. In an address on Faraday by Helmholtz, which I read during my student days in Berlin, the following sentence refers to Faraday’s difficulty just mentioned:

It is generally very difficult to define by a general statement
a new abstraction, so that no misunderstandings of any kind can
arise. The originator of a new concept of that kind finds, as a
rule, that it is much more difficult to find out why other people
do not understand him than it was to discover the new truths.

It was very consoling to me to find out in Berlin from no less an authority than Helmholtz that I was not the only poor mortal who was guessing in vain about the exact meaning of Faraday’s visions.

Newton’s law of gravitation enables the astronomers to calculate accurately from a simple mathematical formula the motion of celestial bodies, without any assumption concerning the mechanism by which gravitational force is transmitted from one body to another body at a distance, say, from the sun to the earth. Newton’s formula says nothing about the time of transmission. The action can be assumed to be direct action at a distance and therefore instantaneous. Experience seemed to indicate that this assumption is correct, because no detectable errors are committed when one assumes that gravitational force travels with infinite velocity. Faraday refused to accept this belief in direct action at a distance for electric and magnetic forces. A few words, only, will suffice to describe how Faraday attempted to eliminate the belief in this direct action at a distance for electrical and magnetic forces. These attempts will always be recorded in history as the first steps in the development of the modern electromagnetic science.

Faraday, starting from points in the electrical and in the magnetic charges, drew numerous curves which indicated at every point in space the direction of the electric or of the magnetic force, and in that manner the whole space surrounding the charges he divided geometrically into _tubular filaments which he called the lines of force_. Every one of these filaments was constructed in accordance with a simple rule, so that it indicated at every point in space not only the direction but also the intensity of the force. A specific example, often employed by me at Arran, will illustrate this. A conducting sphere, say of copper or brass, is charged with positive or with negative electricity. When that charge is in equilibrium it is, as was well known, all on the surface of the sphere and uniformly distributed. Its force of attraction or repulsion, for electrical charges in the space outside of the sphere, is obviously along radii drawn from the centre of the sphere. These radii, drawn in every direction and sufficiently numerous, envelop little cones the vertices of which are at the centre of the sphere. Adjust the size of the cones in such a way that the area of the section of every one of them with the sphere is the same, and make their total number proportional to the charge on the sphere. These little cones are then in this particular case the Faraday lines of force, because their direction gives the direction of the electrical force, and their number per unit area of the surface of any concentric sphere is proportional to the electrical force at any point of the surface of this concentric sphere. According to this picture there are attached to each little element of the total charge a definite number of these conical filaments or lines of force, and each element of the charge on the sphere is nothing more than the terminal of these filaments. When the charge on the sphere is increased or diminished the number of these filaments is also increased or diminished proportionately, and therefore they are more densely or less densely packed in the space which they occupy.

Should the charge on the sphere be set in motion, then the filaments or lines of force attached to it would also move. Thus far I followed Faraday, but went no farther; if I had gone just a little farther I should have met Maxwell. But, unfortunately for me, this simple picture which I constructed, in order to aid my understanding of Faraday’s “Experimental Researches in Electricity” over which I pondered at Arran, suggested nothing more than a mere geometrical representation of the electrical force which the charged sphere exerts at any point in space. It conveyed no additional information which a simple mathematical formula, well-known at that time, did not convey. Additional information, however, was added by Faraday’s imagination, which introduced here what I and many other mortals at that time considered a strange hypothesis. He described the hypothesis at great length in his books, and here is a brief statement of it:

Faraday claimed that all electrical and magnetic actions are transmitted from point to point along his lines of force; and, impelled by a remarkable intuition, he insisted that his lines of force are not mere geometrical pictures but that they had a real physical existence, and that there was something like muscular tension along these lines of force tending to contract them, and a pressure perpendicular to them tending to expand them; and that these tensions and pressures give the same numerical value for the mechanical force between the charges as that calculated from Coulomb’s law, but with the fundamental difference, which Faraday pointed out, that his hypothesis demands a definite finite time for the transmission of electrical and magnetic forces; whereas according to the hypothesis of direct action at a distance, which Coulomb’s law neither favors nor opposes, these forces are transmitted instantaneously. The question of the velocity of transmission of electrical and of magnetic forces through space became, therefore, a crucial question in the decision between the old view and Faraday’s view.

In a letter addressed to Maxwell in 1857, and quoted by Campbell, Faraday said:

I hope this summer to make some experiments on the time of magnetic
action ... that may help the subject on. The time must probably be
short as the time of light; but the greatness of the result, if
affirmative, makes me not despair. Perhaps I had better have said
nothing about it, for I am often long in realizing my intentions,
and a failing memory is against me.

This letter was written ten years before Faraday’s death, and nothing was ever reported about the result of the experiment planned by him. We know, however, that the result which he expected from the experiment was obtained thirty years later by Hertz, a pupil of Helmholtz.

I imagined at Arran that I could hear Faraday say:

Where the lines of magnetic force are there is magnetism, and where
the lines of electric force are there is electricity.

Faraday’s answer to the questions, “What is electricity?” and, “What is magnetism?” was, therefore, according to my understanding at that time, that they were manifestations of force; and where these manifestations exist there is electricity and there is magnetism, in the sense that there are pressures and tensions which are the result of a certain state of the space which may be called the electrical or the magnetic state. Faraday’s visions, as I found them nearly forty years ago, disclosed in his “Experimental Researches in Electricity,” went even so far as to suggest that matter itself consists of centres of force with lines of force proceeding from these centres in every direction to infinite distances, and where these lines are there is the body; in other words, every material body, like every electrical and every magnetic charge, extends to infinity by means of its lines of force; and hence all material bodies are in contact, explicitly denying the existence of ether. No mortal man ever suggested a bolder conception! And yet to-day we know that a conception regarding the structure of matter very similar to that first conceived by Faraday is rapidly gaining universal recognition, not merely as a new metaphysical speculation but as the logical and inexorable demand of experiment. But when Faraday told me all these strange things as I listened attentively on the slope of Goat Fell Mountain at Arran, I could not see anything in them except geometrical pictures and a lot of what appeared to me like pure metaphysics in the background of simple geometrical structures. Although I was sure that Faraday’s metaphysics had some definite physics back of it, I was unable to disentangle it from the hypothetical notions which I did not understand clearly. Maxwell, I thought, must have disentangled that physics, and I often thought of my Scotch friend at Arran who asked me the question: “Can you see in Faraday as far as Maxwell, the Scotchman, saw?”

When I came to Berlin my head was full of Faraday’s lines of force starting at electrical and magnetic charges and winding in all sorts of shapes through space, like stream lines which start from the sources of a river and follow it in its flow toward the ocean. The physical facts and principles which Faraday discovered stood out sharply defined like the bright stars in the firmament of a clear and quiescent summer night; but the conception of the new view of attracting and repelling electric and magnetic forces, which he represented graphically by his lines of force, endowed with strange physical powers residing in pressures and tensions, left in my mind impressions which made me feel that my faith in the new doctrine was not very strong. Faith without conviction is a house built upon sand. Helmholtz said once:

I know too well how often I sat staring hopelessly at his
descriptions of the lines of force, their number and their tensions.

Little I thought during my journey from Arran to Berlin in October, 1885, that two years later all the nebulous notions in my perplexed mind would lift like the mist before the early rays of a sunny autumn morning. I continued my studies of Faraday during my first year in Berlin, reserving for that purpose the necessary time for extra reading. What did the physicists of Berlin think, I wondered, of Faraday’s tubes or lines of force?

I went to Berlin to study experimental physics with Hermann von Helmholtz, the famous professor of physics at the University of Berlin, the formulator of the principle of conservation of energy, and the first interpreter of the meaning of color both in vision and in music and speech. He was then the director of the Physical Institute of the university. His title, conferred upon him by the old Emperor, was Excellenz, and the whole teaching staff of the institute stood in awe when the name of Excellenz was mentioned. The whole scientific world of Germany, nay, the whole intellectual world of Germany, stood in awe when the name of Excellenz von Helmholtz was pronounced. Next to Bismarck and the old Emperor he was at that time the most illustrious man in the German Empire.

I had letters of introduction to him from President Barnard of Columbia College, and also from Professor John Tyndall of the Royal Institution. Professor Arthur Koenig, the right-hand man of Helmholtz and the senior instructor in the Physical Institute, took me to the office of Excellenz von Helmholtz and introduced me as Herr Pupin, a student from America, and the proposed John Tyndall fellow of physics of Columbia College. I was awarded the fellowship three months later. Koenig bowed before his master as if he wished to touch the ground with his forehead. I bowed American fashion, that is, with a bow of the head which did not extend below my shoulders, the same kind of bow which was practised at the University of Cambridge at that time, and I called it the Anglo-Saxon bow; it was entirely different from Koenig’s bow. Helmholtz seemed to notice the difference and he smiled a benevolent smile; the contrast evidently amused him. He had much Anglo-Saxon blood in his veins; his mother was a lineal descendant of William Penn. It was understood in Berlin that he was the most “hoffähig” (presentable at court) scientist in the German Empire.

From a painting by L. Knaus]

He received me kindly and showed deep interest in my proposed plan of study. His appearance was most striking; he was then sixty-four years of age, but looked older. The deep furrows in his face and the projecting veins on the sides and across his towering brow gave him the appearance of a deep introspective thinker, whereas his protruding, scrutinizing eyes marked him a man anxious to penetrate the secrets of nature’s hidden mysteries. The size of his head was enormous, and the muscular neck and huge thorax seemed to form a suitable foundation for such an intellectual dome. His hands and feet were small and beautifully shaped, and his mouth gave evidence of a sweet and gentle disposition. He spoke in the sweetest of accents, and little, but his questions were direct and to the point. When I told him that I never had an opportunity to work in a physical laboratory and had paid exclusive attention to mathematical physics, he smiled and suggested that I should make up this deficiency as soon as possible. “A few experiments successfully carried out usually lead to results more important than all mathematical theories,” he assured me. He then requested Professor Koenig to map out for me a suitable course in the laboratory and to look after me. Koenig did it, and I shall always be grateful to the sadly deformed and extremely kind little man with bushy red hair and distressingly defective eyesight, which he tried to correct with the aid of enormous spectacles employing lenses of extraordinary thickness. Helmholtz was always mellow-hearted to little Koenig, partly because, I think, Koenig reminded him of his own son Robert, who was deformed in hand and foot and back, but had the magnificently shaped head of his distinguished father.

During my first year’s study in Berlin I attended Helmholtz’s lectures on experimental physics. They were most inspiring, not so much on account of the many beautiful experiments which were shown, as on account of the wonderfully suggestive remarks which Helmholtz would drop every now and then under the inspiration of the moment. Helmholtz threw the search-light of his giant intellect upon the meaning of the experiments, and they blazed up like the brilliant colors of a flower garden when a beam of sunlight breaks through the clouds, and tears up the dark shadows which cover the landscape on a cloudy summer day. These lectures were attended not only by students in physics, mathematics, and chemistry, but also by medical students and army officers. The official world, and particularly the army and navy, paid close attention to what Excellenz von Helmholtz had to say; and I had much reason to believe that they consulted his scientific opinions at every step. I have often been called upon to correct the opinion that Helmholtz was a pure scientist par excellence. There is no doubt that his great work dealt principally with fundamental problems in scientific theory and in philosophy; but there is also no doubt that, like many other German scientists, he was much interested in the application of science to the solution of problems which would advance the industries of Germany. His earliest career is associated with his invention of the ophthalmoscope. The optical glass industry of Germany was being developed by some of his former students, who led the world in geometrical optics, a part of physics to which Helmholtz devoted much attention in his younger days.

One day I was on my way to the institute; in front of me walked a tall German army officer, smoking a big cigar. When we reached the entrance of the institute the officer stopped and read a sign which said: “Smoking is strictly forbidden in the institute building.” He threw his cigar away and walked in. I recognized Crown Prince Frederick in the officer. Two years later he became Emperor of Germany and ruled for ninety days. I watched his footsteps and saw that he entered Helmholtz’s office and stayed there over an hour. He undoubtedly consulted the great scientist on some scientific problem which was then interesting the German army and navy.

Helmholtz’s personality was overpowering and seemed to compel one’s interest in problems in which he was interested, and at that time his principal interest was outside of the electromagnetic theory. Nevertheless, I kept up my interest in Faraday, which interest I brought with me from Arran; but I found no opportunity to ascertain Helmholtz’s opinion concerning Faraday. Finally the opportunity came toward the end of my first year at the University of Berlin.

Gustav Robert Kirchhoff, the famous discoverer, formulator, and interpreter of the science of spectrum analysis, and the founder of the theory of radiation, was at that time professor of mathematical physics at the university. He was considered the leading mathematical physicist of Germany. His contributions to the electrical theory occupied a very high place. The most important of these was undoubtedly his theory of transmission of telegraphic signals over a thin wire conductor stretched on insulated poles, high above the ground. It was a magnificent mathematical analysis of the problem, and it showed for the first time that theoretically the velocity of propagation of these signals along the wire is equal to the velocity of light. The university catalogue announced that he was to deliver a course of lectures on theoretical electricity during the first term of my residence at the university. I attended the course and waited and waited, but waited in vain to hear Kirchhoff’s interpretation of Faraday and Maxwell. At the close of the semester the course ended and the electromagnetic theory of Faraday and Maxwell was referred to on two pages only, out of two hundred; and the part so honored was not, even according to my opinion at that time, the essential part of the theory. In this respect the lectures were disappointing, but nevertheless I was most amply rewarded for my pains. I never heard a more elegant mathematical analysis of the old-school electrical problems than that which Kirchhoff developed before his admiring classes. That was the last course of lectures which he delivered; he died in the following year, and was succeeded by Helmholtz as temporary lecturer on mathematical physics.

Helmholtz was rather reserved and could not easily be approached by his students, unless they had some physical problem or a question which was unquestionably worthy of his attention. I made up my mind to ask him, when suitable opportunity presented itself, why Kirchhoff in his lectures paid so little attention to Faraday and Maxwell. It was a very significant sign of those days and I did not understand its meaning. Professor Koenig threw up his hands in holy horror when I informed him of my intention, and prophesied that all kinds of dire consequences would result from my daring proposition; pointing out that such a question would betray a lack of respect on my part both for Kirchhoff and for Helmholtz. Koenig himself could not answer my question except to say that he did not see why the German school of physics should worry much about the English school, particularly when there was a radical difference between the two in the realm of the theory of electromagnetic phenomena. I admitted that if Kirchhoff was the spokesman of the German school then there was a radical difference, intimating however, in the mildest possible way that, in my humble opinion, the difference counted in favor of the English school. I really did not know enough to express that opinion, but I did it under provocation. Koenig flushed up and there would have been quite a lively verbal contest if Helmholtz had not entered my room at that very moment, like a _deus ex machina_. He was making his customary round of visits to the rooms of his research students, in order to find out how their work was moving along. Both Koenig and I looked somewhat perplexed, betraying the fact that we had been engaged in a heated argument, and Helmholtz noticed it. We confessed that we had had a lively discussion; when he learned the subject of our discussion he smiled and referred us both to an address which he had delivered before the Chemical Society of London, five years before. It is entitled, “Recent Developments in Faraday’s Ideas Concerning Electricity.” The same day saw me with two volumes of Helmholtz’s addresses in my hands analyzing his Faraday address. I felt as I went on with this study as if the heavy mist were lifting which had prevented me from seeing a clear view of Faraday’s and Maxwell’s ideas. Tyndall’s fame for clearing up obscure points in physical science was deservedly great, but when I compared Helmholtz’s interpretation of Faraday and Maxwell with that which Tyndall gave me in his book entitled “Faraday as Discoverer,” I marvelled at Helmholtz’s superiority. It must also be remembered that Tyndall was for many years in almost daily contact with Faraday; and, as I pointed out before, he must also have had close personal relations with Maxwell during the period of 1860-1865. To me it seemed a miracle that Helmholtz, a German, saw so much more clearly what was in the minds of two great English philosophers, although he never had met them personally, than did another great English physicist, Tyndall, who knew Faraday and Maxwell personally, and one of them at least intimately. In the article in _Nature_, to which Tyndall first referred me and which Maxwell had written, will be found the following closing paragraph:

Helmholtz is now in Berlin, directing the labors of able men of
science in his splendid laboratory. Let us hope that from his
present position he will again take a comprehensive view of the
waves and ripples of our intellectual progress, and give us from
time to time his idea of the meaning of it all.

Helmholtz’s address on Faraday was one of those comprehensive views of which Maxwell spoke in 1874. Now what did Helmholtz see in Faraday and Maxwell which other physicists, like Tyndall, and even so famous a mathematical physicist as Kirchhoff, failed to see? It was, I thought after a careful study of Helmholtz’s address, the simplest thing in the world, particularly for one who, like myself, had been wrestling with Faraday’s lines of force, and with the hypothetical powers with which Faraday had endowed them. So simple, indeed, that I venture to describe it here. But in order to make the description as brief and as simple as possible I must go back again to the charged spherical conductor which always rendered good service in those days when I was trying to solve the riddle of Faraday’s new physical concepts.

By means of an electrical force generated by an electrical machine we can increase or diminish the charge on the surface of the conducting sphere. Now, the charge on the sphere increases or diminishes because the electrical force generated by the machine drives through a suitable conducting wire additional electrical charge to the sphere, or takes it away from it. This motion of the electrical charge through the conducting wire to or from the sphere is the electrical current. Here comes now the historic question: Does the electrical current stop at the surface of the charged sphere? The old electrical theories said “Yes,” but Maxwell, interpreting the ideas of Faraday, said, “No.” Helmholtz was the first to tell me that clearly and distinctly, and I understood him.

Since, according to Faraday, each particle of the charge on the sphere carries attached to it a definite number of filaments or lines of force, it is obvious that the rate at which the charge on the sphere increases is, as I described above, the same as the rate at which the number of these lines of force are crowded into the space surrounding the sphere. Motion of the charge to the surface of the sphere is accompanied by a motion of the Faraday lines of force through every surface which surrounds the charged sphere. Since, according to Faraday, electricity is everywhere where the lines of force are, it follows that the motion of the lines through any surface means motion of electricity (in the sense in which I use this word) through that surface. Maxwell said, according to my understanding of Helmholtz, that motion of electricity, as represented by the motion of Faraday’s lines of force, is an electrical current just as much as the motion of electrical charges is. Electrical charges are terminals, only, of the lines of force; and why should the motion of the terminals be endowed with a power which is denied to the remaining parts of the lines of force? The principal power is, according to Oerstedt’s discovery, the generation of magnetism; that is, magnetic lines of force. According to Maxwell, then, the electrical current (that is, the motion of electrical charges through conductors) does not stop at the surface of the conductor, but continues in the non-conducting space beyond as motion of Faraday’s lines of force, as _motion of electricity_. The extension of the meaning of the word electrical current, just described, was, according to Helmholtz, the cardinal difference between the old electrical theories and the Faraday-Maxwell electromagnetic theory, and Helmholtz declared in favor of the last. I applauded Helmholtz and took off my hat to his clear vision of things which other people, including myself, failed to see. But can any one blame ordinary mortals, who were always accustomed to look upon the electrical current as motion of electrical charges in conductors, when they failed to see that the electrical current can take place even in a vacuum where there are no electrical charges at all, and therefore no motion of them? That was the physical concept which found its way so slowly into minds polarized by preconceived notions even after Helmholtz’s lucid explanation. This is substantially all there is in the Faraday-Maxwell electromagnetic theory as I gathered it directly from the Helmholtz address. But there is another very important element which I ought to describe here.

A corollary of Maxwell’s extension of the meaning of electrical current, which Helmholtz did not mention explicitly but which I soon found in Maxwell, is this: Electrical charges move because a force acts upon them; similarly the number of Faraday’s lines of force, passing through any surface in space, increases or diminishes because there is a force acting upon them. Wherever there is an action there is an equal and opposite reaction, according to the most fundamental law of Newton’s dynamics. Hence space, including the vacuum, must react when Faraday’s lines of force (that is, when the electricity represented by them) move through it. But if this reaction really exists in space, how can it be expressed? Faraday and Maxwell devoted much thought and many experimental investigations in search for a definite answer to this question, and they found it.

Faraday showed by experiment that if the charged sphere is immersed in an insulating fluid, say an insulating mineral oil, or in a solid insulator like rubber, or even if a piece of an insulator is brought near it, then the reacting force for a given charge on the sphere is smaller than when the sphere is surrounded by a vacuum; or, in other words, liquid and solid insulators are more _permeable_ to the electrical lines of force (that is, to electricity) than a vacuum is. Therefore, an electrical force which is acting in order to increase the charge on the sphere and, as a result, increase the number of lines of force through the surrounding space, will experience the less reaction the more permeable the surrounding medium is. The reaction of an insulator against the action of an electrical force appears therefore as a reaction against the passage of electricity, that is, of electrical lines of force, through it. That picture of the process has stayed with me ever since my Berlin days.

The same line of reasoning which I followed above, regarding electrical lines of force, leads to similar results with regard to the magnetic lines of force. The reaction of the medium against an increase of the electrical and of the magnetic lines of force through it was the second new physical concept introduced into the electrical science by Faraday and Maxwell.