James Clerk Maxwell, the first professor of experimental physics at
Cambridge, was born at Edinburgh on November 13, 1831, and before
he was fifteen was already famous as a writer of scientific papers.
In 1854 he graduated at Cambridge as second wrangler. Two years
later he became professor of natural philosophy at Marischal
College, Aberdeen. Vacating his chair in 1860 for one at King's
College, London, Maxwell contributed largely to scientific
literature. His great lifework, however, is his famous "Treatise on
Electricity and Magnetism," which was published in 1873, and is, in
the words of a critic, "one of the most splendid monuments ever
raised by the genius of a single individual." It was in this work
that he constructed his famous theory if electricity in which
"action at a distance" should be replaced by "action through a
medium," and first enunciated the principles of an electro-magnetic
theory of light which has formed the basis of nearly all modern
physical science. He died on November 5, 1879.
_I.--The Nature of Electricity_
Let a piece of glass and a piece of resin be rubbed together. They will
be found to attract each other. If a second piece of glass be rubbed
with a second piece of resin, it will be found that the two pieces of
glass repel each other and that the two pieces of resin are also
repelled from one another, while each piece of glass attracts each piece
of resin. These phenomena of attraction and repulsion are called
electrical phenomena, and the bodies which exhibit them are said to be
"electrified," or to be "charged with electricity."
Bodies may be electrified in many other ways, as well as by friction.
When bodies not previously electrified are observed to be acted on by an
electrified body, it is because they have become "electrified by
induction." If a metal vessel be electrified by induction, and a second
metallic body be suspended by silk threads near it, and a metal wire be
brought to touch simultaneously the electrified body and the second
body, this latter body will be found to be electrified. Electricity has
been transferred from one body to the other by means of the wire.
There are many other manifestations of electricity, all of which have
been more or less studied, and they lead to the formation of theories of
its nature, theories which fit in, to a greater or less extent, with the
observed facts. The electrification of a body is a physical quantity
capable of measurement, and two or more electrifications can be combined
experimentally with a result of the same kind as when two quantities are
added algebraically. We, therefore, are entitled to use language fitted
to deal with electrification as a quantity as well as a quality, and to
speak of any electrified body as "charged with a certain quantity of
positive or negative electricity."
While admitting electricity to the rank of a physical quantity, we must
not too hastily assume that it is, or is not, a substance, or that it
is, or is not, a form of energy, or that it belongs to any known
category of physical quantities. All that we have proved is that it
cannot be created or annihilated, so that if the total quantity of
electricity within a closed surface is increased or diminished, the
increase or diminution must have passed in or out through the closed
surface.
This is true of matter, but it is not true of heat, for heat may be
increased or diminished within a closed surface, without passing in or
out through the surface, by the transformation of some form of energy
into heat, or of heat into some other form of energy. It is not true
even of energy in general if we admit the immediate action of bodies at
a distance.
There is, however, another reason which warrants us in asserting that
electricity, as a physical quantity, synonymous with the total
electrification of a body, is not, like heat, a form of energy. An
electrified system has a certain amount of energy, and this energy can
be calculated. The physical qualities, "electricity" and "potential,"
when multiplied together, produce the quantity, "energy." It is
impossible, therefore, that electricity and energy should be quantities
of the same category, for electricity is only one of the factors of
energy, the other factor being "potential."
Electricity is treated as a substance in most theories of the subject,
but as there are two kinds of electrification, which, being combined,
annul each other, a distinction has to be drawn between free electricity
and combined electricity, for we cannot conceive of two substances
annulling each other. In the two-fluid theory, all bodies, in their
unelectrified state, are supposed to be charged with equal quantities of
positive and negative electricity. These quantities are supposed to be
so great than no process of electrification has ever yet deprived a body
of all the electricity of either kind. The two electricities are called
"fluids" because they are capable of being transferred from one body to
another, and are, within conducting bodies, extremely mobile.
In the one-fluid theory everything is the same as in the theory of two
fluids, except that, instead of supposing the two substances equal and
opposite in all respects, one of them, generally the negative one, has
been endowed with the properties and name of ordinary matter, while the
other retains the name of the electric fluid. The particles of the fluid
are supposed to repel each other according to the law of the inverse
square of the distance, and to attract those of matter according to the
same law. Those of matter are supposed to repel each other and attract
those of electricity. This theory requires us, however, to suppose the
mass of the electric fluid so small that no attainable positive or
negative electrification has yet perceptibly increased or diminished the
mass or the weight of a body, and it has not yet been able to assign
sufficient reasons why the positive rather than the negative
electrification should be supposed due to an _excess_ quantity of
electricity.
For my own part, I look for additional light on the nature of
electricity from a study of what takes place in the space intervening
between the electrified bodies. Some of the phenomena are explained
equally by all the theories, while others merely indicate the peculiar
difficulties of each theory. We may conceive the relation into which the
electrified bodies are thrown, either as the result of the state of the
intervening medium, or as the result of a direct action between the
electrified bodies at a distance. If we adopt the latter conception, we
may determine the law of the action, but we can go no further in
speculating on its cause.
If, on the other hand, we adopt the conception of action through a
medium, we are led to inquire into the nature of that action in each
part of the medium. If we calculate on this hypothesis the total energy
residing in the medium, we shall find it equal to the energy due to the
electrification of the conductors on the hypothesis of direct action at
a distance. Hence, the two hypotheses are mathematically equivalent.
On the hypothesis that the mechanical action observed between
electrified bodies is exerted through and by means of the medium, as the
action of one body on another by means of the tension of a rope or the
pressure of a rod, we find that the medium must be in a state of
mechanical stress. The nature of the stress is, as Faraday pointed out,
a tension along the lines of force combined with an equal pressure in
all directions at right angles to these lines. This distribution of
stress is the only one consistent with the observed mechanical action on
the electrified bodies, and also with the observed equilibrium of the
fluid dielectric which surrounds them. I have, therefore, assumed the
actual existence of this state of stress.
Every case of electrification or discharge may be considered as a
motion in a closed circuit, such that at every section of the circuit
the same quantity of electricity crosses in the same time; and this is
the case, not only in the voltaic current, where it has always been
recognised, but in those cases in which electricity has been generally
supposed to be accumulated in certain places. We are thus led to a very
remarkable consequence of the theory which we are examining, namely,
that the motions of electricity are like those of an _incompressible_
fluid, so that the total quantity within an imaginary fixed closed
surface remains always the same.
The peculiar features of the theory as developed in this book are as
follows.
That the energy of electrification resides in the dielectric medium,
whether that medium be solid or gaseous, dense or rare, or even deprived
of ordinary gross matter, provided that it be still capable of
transmitting electrical action.
That the energy in any part of the medium is stored up in the form of a
constraint called polarisation, dependent on the resultant electromotive
force (the difference of potentials between two conductors) at the
place.
That electromotive force acting on a dielectric produces what we call
electric displacement.
That in fluid dielectrics the electric polarisation is accompanied by a
tension in the direction of the lines of force combined with an equal
pressure in all directions at right angles to the lines of force.
That the surfaces of any elementary portion into which we may conceive
the volume of the dielectric divided must be conceived to be
electrified, so that the surface density at any point of the surface is
equal in magnitude to the displacement through that point of the surface
_reckoned inwards_.
That, whatever electricity may be, the phenomena which we have called
electric displacement is a movement of electricity in the same sense as
the transference of a definite quantity of electricity through a wire.
_II.--Theories of Magnetism_
Certain bodies--as, for instance, the iron ore called loadstone, the
earth itself, and pieces of steel which have been subjected to certain
treatment--are found to possess the following properties, and are called
magnets.
If a magnet be suspended so as to turn freely about a vertical axis, it
will in general tend to set itself in a certain azimuth, and, if
disturbed from this position, it will oscillate about it.
It is found that the force which acts on the body tends to cause a
certain line in the body--called the axis of the magnet--to become
parallel to a certain line in space, called the "direction of the
magnetic force."
The ends of a long thin magnet are commonly called its poles, and like
poles repel each other; while unlike poles attract each other. The
repulsion between the two magnetic poles is in the straight line joining
them, and is numerically equal to the products of the strength of the
poles divided by the square of the distance between them; that is, it
varies as the inverse square of the distance. Since the form of the law
of magnetic action is identical with that of electric action, the same
reasons which can be given for attributing electric phenomena to the
action of one "fluid," or two "fluids" can also be used in favour of the
existence of a magnetic matter, fluid or otherwise, provided new laws
are introduced to account for the actual facts.
At all parts of the earth's surface, except some parts of the polar
regions, one end of a magnet points in a northerly direction and the
other in a southerly one. Now a bar of iron held parallel to the
direction of the earth's magnetic force is found to become magnetic. Any
piece of soft iron placed in a magnetic field is found to exhibit
magnetic properties. These are phenomena of _induced_ magnetism. Poisson
supposes the magnetism of iron to consist in a separation of the
magnetic fluids within each magnetic molecule. Weber's theory differs
from this in assuming that the molecules of the iron are always magnets,
even before the application of the magnetising force, but that in
ordinary iron the magnetic axes of the molecules are turned
indifferently in every direction, so that the iron as a whole exhibits
no magnetic properties; and this theory agrees very well with what is
observed.
The theories establish the fact that magnetisation is a phenomenon, not
of large masses of iron, but of molecules; that is to say, of portions
of the substance so small that we cannot by any mechanical method cut
them in two, so as to obtain a north pole separate from the south pole.
We have arrived at no explanation, however, of the nature of a magnetic
molecule, and we have therefore to consider the hypothesis of
Ampère--that the magnetism of the molecule is due to an electric current
constantly circulating in some closed path within it.
Ampère concluded that if magnetism is to be explained by means of
electric currents, these currents must circulate within the molecules of
the magnet, and cannot flow from one molecule to another. As we cannot
experimentally measure the magnetic action at a point within the
molecule, this hypothesis cannot be disproved in the same way that we
can disprove the hypothesis of sensible currents within the magnet. In
spite of its apparent complexity, Ampère's theory greatly extends our
mathematical vision into the interior of the molecules.
_III.--The Electro-Magnetic Theory of Light_
We explain electro-magnetic phenomena by means of mechanical action
transmitted from one body to another by means of a medium occupying the
space between them. The undulatory theory of light also assumes the
existence of a medium. We have to show that the properties of the
electro-magnetic medium are identical with those of the luminiferous
medium.
To fill all space with a new medium whenever any new phenomena are to be
explained is by no means philosophical, but if the study of two
different branches of science has independently suggested the idea of a
medium; and if the properties which must be attributed to the medium in
order to account for electro-magnetic phenomena are of the same kind as
those which we attribute to the luminiferous medium in order to account
for the phenomena of light, the evidence for the physical existence of
the medium is considerably strengthened.
According to the theory of emission, the transmission of light energy is
effected by the actual transference of light-corpuscles from the
luminous to the illuminated body. According to the theory of undulation
there is a material medium which fills the space between the two bodies,
and it is by the action of contiguous parts of this medium that the
energy is passed on, from one portion to the next, till it reaches the
illuminated body. The luminiferous medium is therefore, during the
passage of light through it, a receptacle of energy. This energy is
supposed to be partly potential and partly kinetic, and our theory
agrees with the undulatory theory in assuming the existence of a medium
capable of becoming a receptacle for two forms of energy.
Now, the properties of bodies are capable of quantitative measurement.
We therefore obtain the numerical value of some property of the
medium--such as the velocity with which a disturbance is propagated in
it, which can be calculated from experiments, and also observed directly
in the case of light. If it be found that the velocity of propagation of
electro-magnetic disturbance is the same as the velocity of light, we
have strong reasons for believing that light is an electro-magnetic
phenomenon.
It is, in fact, found that the velocity of light and the velocity of
propagation of electro-magnetic disturbance are quantities of the same
order of magnitude. Neither of them can be said to have been determined
accurately enough to say that one is greater than the other. In the
meantime, our theory asserts that the quantities are equal, and assigns
a physical reason for this equality, and it is not contradicted by the
comparison of the results, such as they are.
Lorenz has deduced from Kirchoff's equations of electric currents a new
set of equations, indicating that the distribution of force in the
electro-magnetic field may be considered as arising from the mutual
action of contiguous elements, and that waves, consisting of transverse
electric currents, may be propagated, with a velocity comparable with
that of light, in non-conducting media. These conclusions are similar to
my own, though obtained by an entirely different method.
The most important step in establishing a relation between electric and
magnetic phenomena and those of light must be the discovery of some
instance in which one set of phenomena is affected by the other. Faraday
succeeded in establishing such a relation, and the experiments by which
he did so are described in the nineteen series of his "Experimental
Researches." Suffice it to state here that he showed that in the case of
aray of plane-polarised light the effect of the magnetic force is to
turn the plane of polarisation round the direction of the ray as an
axis, through a certain angle.
The action of magnetism on polarised light leads to the conclusion that
in a medium under the action of a magnetic force, something belonging to
the same mathematical class as an angular velocity, whose axis is in the
direction of the magnetic force, forms part of the phenomenon. This
angular velocity cannot be any portion of the medium of sensible
dimensions rotating as a whole. We must, therefore, conceive the
rotation to be that of very small portions of the medium, each rotating
on its own axis.
This is the hypothesis of molecular vortices. The displacements of the
medium during the propagation of light will produce a disturbance of the
vortices, and the vortices, when so disturbed, may react on the medium
so as to affect the propagation of the ray. The theory proposed is of a
provisional kind, resting as it does on unproved hypotheses relating to
the nature of molecular vortices, and the mode in which they are
affected by the displacement of the medium.
_IV.--Action at a Distance_
There appears to be some prejudice, or _a priori_ objection, against the
hypothesis of a medium in which the phenomena of radiation of light and
heat, and the electric actions at a distance, take place. It is true
that at one time those who speculated as to the cause of physical
phenomena were in the habit of accounting for each kind of action at a
distance by means of a special æthereal fluid, whose function and
property it was to produce these actions. They filled all space three
and four times over with æthers of different kinds, the properties of
which consisted merely to "save appearances," so that more rational
inquirers were willing to accept not only Newton's definite law of
attraction at a distance, but even the dogma of Cotes that action at a
distance is one of the primary properties of matter, and that no
explanation can be more intelligible than this fact. Hence the
undulatory theory of light has met with much opposition, directed not
against its failure to explain the phenomena, but against its assumption
of the existence of a medium in which light is propagated.
The mathematical expression for electro-dynamic action led, in the mind
of Gauss, to the conviction that a theory of the propagation of electric
action would in time be found to be the very keystone of
electro-dynamics. Now, we are unable to conceive of propagation in time,
except either as the flight of a material substance through space or as
the propagation of a condition of motion or stress in a medium already
existing in space.
In the theory of Neumann, the mathematical conception called potential,
which we are unable to conceive as a material substance, is supposed to
be projected from one particle to another, in a manner which is quite
independent of a medium, and which, as Neumann has himself pointed out,
is extremely different from that of the propagation of light. In other
theories it would appear that the action is supposed to be propagated in
a manner somewhat more similar to that of light.
But in all these theories the question naturally occurs: "If something
is transmitted from one particle to another at a distance, what is its
condition after it had left the one particle, and before it reached the
other?" If this something is the potential energy of the two particles,
as in Neumann's theory, how are we to conceive this energy as existing
in a point of space coinciding neither with the one particle nor with
the other? In fact, whenever energy is transmitted from one body to
another in time, there must be a medium or substance in which the energy
exists after it leaves one body, and before it reaches the other, for
energy, as Torricelli remarked, "is a quintessence of so subtile a
nature that it cannot be contained in any vessel except the inmost
substance of material things."
Hence all these theories lead to the conception of a medium in which the
propagation takes place, and if we admit this medium as an hypothesis, I
think we ought to endeavour to construct a mental representation of all
the details of its action, and this has been my constant aim in this
treatise.