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.
[Illustration: HERMAN VON HELMHOLTZ
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.
The Faraday-Maxwell electromagnetic theory extended the well-known
electrical and magnetic actions and reactions from conductors to
non-conductors, including the vacuum. If this theory is correct, then
electromagnetic disturbances will be propagated from their source to
all parts of space, and not along conductors only, by definite waves
travelling at a definite velocity.
Maxwell’s calculation showed that electromagnetic disturbances
are propagated through insulators in the same manner as light is
propagated, and that, therefore, _light is in all probability an
electromagnetic disturbance_. This is the substance of Maxwell’s
electromagnetic theory of light; it is his answer to the question:
“What is Light?”
That, broadly stated, was the information which Helmholtz first
conveyed to me in terms which I understood clearly; and for this
service I have always been profoundly grateful to him. He showed me
that the Faraday-Maxwell electromagnetic theory was incomparably
simpler than I thought it to be, and also much more beautiful. I do not
believe that in 1881 there was another physicist in continental Europe
who could have given me that information, and perhaps not even in 1886,
when I first read that wonderful address. My friend Niven in Cambridge,
editor of the second edition of Maxwell’s great mathematical treatise,
never volunteered to tell me how Maxwell answered the question: “What
is Light?” Neither did Tyndall. I do not know whether Rayleigh or
Stokes or anybody else in Cambridge when I was there could have done it
as well as Helmholtz did. I shall describe later an historical event
which indicates that they probably could not.