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.
[Illustration: _From a photograph by John Watkins, London_
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.