DEVELOPMENT OF MAXWELL’S THEORY.
We have endeavoured in the preceding pages to give some account of
Maxwell’s contributions to electrical theory and the physics of the
ether. We must now consider very briefly what evidence there is to
support these views. At Maxwell’s death such evidence, though strong,
was indirect. His supporters were limited to some few English-speaking
pupils, young and enthusiastic, who were convinced, it may be, in no
small measure, by the affection and reverence with which they regarded
their master. Abroad his views had made very little way.
In the last words of his book he writes, speaking of various
distinguished workers--
“There appears to be in the minds of these eminent men some
prejudice, or _à 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
causes of physical phenomena were in the habit of accounting
for each kind of action at a distance by means of a special
ætherial 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 were
invented merely to ‘save appearances,’ so that more rational
enquirers were willing rather to accept not only Newton’s
definite law of attraction at a distance, but even the dogma
of Cotes,[64] 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.
“We have seen that 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 in time would be found to be the very key-stone 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 the theories of Riemann and Betti it would appear that the
action is supposed to be propagated in a manner somewhat more
similar to that of light.
“But in all of these theories the question naturally
occurs:--If something is transmitted from one particle to
another at a distance, what is its condition after it has
left one particle and before it has 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[65] remarked, ‘is a quintessence of so subtle a
nature that it cannot be contained in any vessel except the
inmost substance of material things.’ Hence all these theories
lead to a conception of a medium in which the propagation takes
place, and if we admit this medium as an hypothesis, I think
it ought to occupy a prominent place in our investigations,
and that 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.”
Let us see, then, what were the experimental grounds in Maxwell’s day
for accepting as true his views on electrical action, and how since
then, by the genius of Heinrich Hertz and the labours of his followers,
those grounds have been rendered so sure that nearly the whole progress
of electrical science during the last twenty years has consisted in
the development of ideas which are to be found in the “Treatise on
Electricity and Magnetism.”
The purely electrical consequences of Maxwell’s theory were of course
in accord with all known electrical observations. The equations of the
field accounted for the electro-magnetic forces observed in various
experiments, and from them the laws of electro-magnetic induction
could be correctly deduced; but there was nothing very special in
this. Similar equations had been obtained from the theory of action at
a distance by various writers; in fact, Helmholtz’s theory, based on
the most general form of expression for the force between two elements
of current consistent with certain experiments of Ampère’s, was more
general in its character than Maxwell’s. The destructive features of
Maxwell’s theory were:
(1) The assumption that all currents flow in closed circuits.
(2) The idea of energy residing throughout the electro-magnetic
field in consequence of the strains and stresses set up in the
electro-magnetic medium by the actions to which it was subject.
(3) The identification of this electro-magnetic medium with the
luminiferous ether, and the consequent view that light is an
electro-magnetic phenomena.
(4) The view that electro-magnetic forces arise entirely from strains
and stresses set up in the ether; the electrostatic charge of an
insulated conductor being one of the forms in which the ether strain is
manifested to us.
(5) A dielectric under the action of electric force is said to
become polarised, and, according to Maxwell (vol. i. p. 133), all
electrification is the residual effect of the polarisation of the
dielectric.
Now it must, I think, be admitted that in Maxwell’s day there was
direct proof of very few of these propositions. No one has even yet so
measured the displacement currents in a dielectric as to show that the
total flow across every section of a circuit is at any given moment
the same, though there are other experiments of an indirect character
which have now completely justified Maxwell’s hypothesis. Experiments
by Schiller and Von Helmholtz prove it is true that some action in
the dielectric must be taken into consideration in any satisfactory
theory; they therefore upset various theories based on direct action at
a distance, “but they tell us nothing as to whether any special form
of the dielectric theory, such as Maxwell’s or Helmholtz’s, is true or
not.” (J. J. Thomson, “Report on Electrical Theories,” B.A. Report,
1885, p. 149.)
When Maxwell died there had been little if any experimental evidence
as to the stresses set up in a body by electric force. Fontana, Govi,
and Duter had all observed that changes take place in the volume of
the dielectric of a condenser when it is charged. Quincke had taken
up the work, and the first of his classic papers on this subject was
published in 1880, the year following Maxwell’s death. Maxwell himself
was fond of shewing an experiment in which a charged insulated sphere
was brought near to the surface of paraffin; the stress on the surface
causes a heaping up of the paraffin under the sphere.
Kerr had shewn in 1875 that many substances become doubly refracting
under electric stress; his complete determination of the laws of this
action was published at a later date.
As to direct measurements on electric waves, there were none; the value
of the velocity with which, if Maxwell’s theory were true, they must
travel had been determined from electrical observations of quite a
different character. Weber and Kohlrausch had measured the value of K
for air, for which μ is unity, and from their observations it follows
that the value of the wave velocity for electro-magnetic waves is about
31 × 10⁹ centimetres per second. The velocity of light was known, from
the experiments of Fizeau and Foucault, to have about this value, and
it was the near coincidence of these two values which led Maxwell to
write in 1864:--
“The agreement of the results seems to show that light and magnetism
are affections of the same substance, and that light is an
electro-magnetic disturbance propagated through the field according to
electro-magnetic laws.”
By the time the first edition of the “Electricity and Magnetism”
was published, Maxwell and Thomson (Lord Kelvin) had both made
determinations of K, and had shewn that for air at least the resulting
value for the velocity of electro-magnetic waves was very nearly that
of light.
For other substances at that date the observations were fewer still.
Gibson and Barclay had determined the specific inductive capacity
of paraffin, and found that its square root was 1·405, while its
refractive index for long waves is 1·422. Maxwell himself thought
that if a similar agreement could be shewn to hold for a number of
substances, we should be warranted in concluding that “the square root
of K, though it may not be the complete expression for the index of
refraction, is at least the most important term in it.”
Between this time and Maxwell’s death enough had been done to more
than justify this statement. It was clear from the observations of
Boltzmann, Silow, Hopkinson, and others that there were many substances
for which the square root of the specific inductive capacity was very
nearly indeed equal to the refractive index, and good reason had been
given why in some cases there should be a considerable difference
between the two.
Hopkinson found that in the case of glass the differences were very
large, and they have since been found to be considerable for most
solids examined, with the exception of paraffin and sulphur. For
petroleum oil, benzine, toluene, carbon-bisulphide, and some other
liquids the agreement between Maxwell’s theory and experiment is
close. For the fatty oils, such as castor oil, olive oil, sperm oil,
neatsfoot oil, and also for ether, the differences are considerable.
It seems probable that the reason for this difference lies in the
fact that, in the light waves, we are dealing with the wave velocity
of a disturbance of an extremely short period. Now, we know that the
substances mentioned shew optical dispersion, and we have at present
no completely satisfactory theory from which we can calculate, from
experiments on very short waves, what the velocity for very long
waves will be. In most cases Cauchy’s formula has been used to obtain
the numbers given. The value of K, however, as found by experiment,
corresponds to these infinitely long waves, and to quote Professor
J. J. Thomson’s words, “the marvel is not that there should not be
substances for which the relation K = μ² does not hold, but that there
should be any for which it does.”[66]
It has been shewn, moreover, both by Professor J. J. Thomson himself
and by Blondlot, that when the value of K is measured under very
rapidly varying electrifications, changing at the rate of about
25,000,000 to the second, the value of the inductive capacity for glass
is reduced from about 6·8 or 7 to about 2·7; the square root of this is
1·6, which does not differ much from its refractive index. The values
of the inductive capacity of paraffin and sulphur, which it will be
remembered agree fairly with Maxwell’s theory, were found to be not
greatly different in the steady and in the rapidly varying field.
On the other hand, some experiments of Arons and Rubens in rapidly
varying fields lead to values which do not differ greatly from those
given by other methods. The theory, however, of these experiments seems
open to criticism.
To attempt anything like a complete account of modern verifications
of Maxwell’s views and modern developments of his theory is a task
beyond our limits, but an account of Maxwell written in 1895 would be
incomplete without a reference to the work of Heinrich Hertz.
Maxwell told us what the properties of electro-magnetic waves in air
must be. Hertz[67] in 1887 enabled us to measure those properties, and
the measurements have verified completely Maxwell’s views.
The method of producing electrical oscillations in a conductor had
long been known. Thomson and Von Helmholtz had both pointed it out.
Schiller had examined such oscillations in 1874, and had determined the
inductive capacity of glass by their means, using oscillations whose
period varied from ·000056 to ·00012 of a second.
These oscillations were produced by discharging a condenser through a
coil of wire having self-induction. If the electrical resistance of the
coil be not too great, the charge oscillates backwards and forwards
between the plates of the condenser until its energy is dissipated in
the heat produced in the wire, and in the electro-magnetic radiations
which leave it.
The period of these oscillations under proper conditions is given by
the formula T = 2π√(CL) where L, the coefficient of self induction,
and _C_ the capacity of the condenser. These quantities can be
calculated, and hence the time of an oscillation is known. From such
an arrangement waves radiate out into space. If we could measure
by any method the length of such a wave we could determine its
velocity by dividing the wave length by the period. But it is clear
that since the velocity is comparable with that of light the wave
length will be enormous, unless the period is very short. Thus, a
wave, travelling with the velocity of light, whose period was ·0001
second, such as the waves Schiller worked with, would have a length of
·0001 × 30,000,000,000 or 3,000,000 centimetres, and would be quite
unmeasurable. Before measurements on electric waves could be made it
was necessary (1) to produce waves of sufficiently rapid period, (2) to
devise means to detect them. This is what Hertz did.
The wave length of the electrical oscillations can be reduced by
reducing either the electrical capacity of the system, or the
coefficient of self-induction of the wire. Hertz adopted both these
expedients. His vibrator, in some of his more important experiments,
consisted of two square brass plates 40 cm. in the side. To each of
these is attached a piece of copper wire about 30 cm. in length, and
each wire ends in a small highly-polished brass ball. The plates are
placed so that the wires lie in the same straight line, the brass
balls being separated by a very small air gap. The two plates are then
charged, the one positively the other negatively, until the insulation
resistance of the air gap breaks down and a discharge passes across.
Under these conditions the discharge is oscillatory. It does not
consist of a single spark, but of a series of sparks, which pass
and repass in opposite directions, until the energy of the original
charge is radiated into space or dissipated as heat; the plates are
then recharged and the process repeated. In Hertz’s experiments the
oscillator was charged by being connected to the secondary terminals of
an induction coil.
In 1883 Professor Fitzgerald had called attention to this method of
producing electric waves in air, and had given two metres as the
minimum wave length which might be attained. In 1870 Herr von Bezold
had actually made observations on the propagation and reflection of
electrical oscillations, but his work, published as a preliminary
communication, had attracted little notice. Hertz was the first to
undertake in 1887 in a systematic manner the investigation of the
electric waves in air which proceed from such an oscillator with a view
to testing various theories of electro-magnetic action.
It remained, however, necessary to devise an apparatus for detecting
the waves. When the waves are incident on a conductor, electric
surgings are set up in the conductor, and may, under proper conditions,
be observed as tiny sparks. Hertz used as his detector a loop of wire,
the ends of which terminated in two small brass balls. The wire was
bent so that the balls were very close together, and the sparks could
be seen passing across the tiny air gap which separated them. Such
a wire will have a definite period of its own for oscillations of
electricity with which it may be charged, and if the frequency of the
electric waves which fall on it agrees with that of the waves which
it can itself emit, the oscillations which are set up in the wire will
be stronger than under other conditions, the sparks seen will be more
brilliant.[68] Hertz’s resonator was a circle of wire thirty-five
centimetres in radius, the period for such a resonator would, he
calculated, be the same as that of his vibrator.
There is, however, very considerable difficulty in determining the
period of an electric oscillator from its dimensions, and the value
obtained from calculation for that of Hertz’s radiator is not very
trustworthy. The complete period is, however, comparable with two
one hundredth millionths of a second; in his original papers, Hertz,
through an error, gave a value greater than this.
With these arrangements Hertz was able to detect the presence of
electrical radiation at considerable distances from the radiator; he
was also able to measure its wave length. In the case of sound waves
the existence of nodes and loops formed under proper conditions is
well known. When waves are directly reflected from a flat surface,
interference takes place between the incident and reflected waves,
stationary vibrations are set up, and nodes and loops--places, that
is, of minimum and of maximum motion respectively--are formed. The
position of these nodes and loops can be determined by the aid of
suitable apparatus, and it can be shewn that the distance between two
consecutive nodes is half the wave length.
Similarly when electrical vibrations fall on a reflector, a large
flat surface of metal, for example, stationary vibrations due to the
interference between the incident and reflected waves are produced, and
these give rise to electrical nodes and loops. The position of such
nodes and loops can be found by the use of Hertz’s apparatus, or in
other ways, and hence the length of the electrical waves can be found.
The existence of the nodes and loops shews that the electric effects
are propagated by wave motion. The length of the waves is found to be
definite, since the nodes and loops recur at equal intervals apart.
If it be assumed that the frequency is known, the velocity of wave
propagation can be determined. Hertz found from his experiments that
in air the waves travelled with the velocity of light. It appears,
however, that there were two errors in the calculation which happened
to correct each other, so that neither the value of the frequency given
in Hertz’s paper nor the wave length observed is correct.
By modifying the apparatus it was possible to measure the wave length
of the waves transmitted along a copper wire, and hence, again
assuming the period of oscillation, to calculate the velocity of wave
propagation along the wire. Hertz made the experiment, and found from
his first observations that the waves were propagated along the wire
with a finite velocity, but that the velocity differed from that in
air. The half-wave length in the wire was only about 2·8 metres; that
in air was about 4·5 metres.
Now, this experiment afforded a crucial test between the theories of
Maxwell and Von Helmholtz. According to the former, the waves do not
travel in the wire at all; they travel through the air alongside the
wire, and the wave length observed by Hertz ought to have been the same
as in air. According to Von Helmholtz, the two velocities observed
by Hertz should have been different, as, indeed, they were, and the
experiment appeared to prove that Maxwell’s theory was insufficient and
that a more general one, such as that of Von Helmholtz, was necessary.
But other experiments have not led to the same result. Hertz himself,
using more rapid oscillations in some later measurements, found that
the wave length of the electric waves from a given oscillator was the
same whether they were transmitted through free space or conducted
along a wire.[69] Lecher and J. J. Thomson have arrived at the same
result; but the most complete experiments on this point are those of
Sarasin and De la Rive.
It may be taken, then, as established that Maxwell’s theory is
sufficient, and that the greater generality of Von Helmholtz is
unnecessary.
In a later paper Hertz showed that electric waves could be reflected
and refracted, polarised and analysed, just like light waves. In his
introduction to his “Collected Papers” he writes (p. 19):--
“Casting now a glance backwards, we see that by the experiments
above sketched the propagation in time of a supposed action
at a distance is for the first time proved. This fact forms
the philosophic result of the experiments, and indeed, in a
certain sense, the most important result. The proof includes
a recognition of the fact that the electric forces can
disentangle themselves from material bodies, and can continue
to subsist as conditions or changes in the state of space. The
details of the experiments further prove that the particular
manner in which the electric force is propagated exhibits the
closest analogy[70] with the propagation of light; indeed, that
it corresponds almost completely to it. The hypothesis that
light is an electrical phenomenon is thus made highly probable.
To give a strict proof of this hypothesis would logically
require experiments upon light itself.
“What we here indicate as having been accomplished by the
experiments is accomplished independently of the correctness
of particular theories. Nevertheless, there is an obvious
connection between the experiments and the theory in connection
with which they were really undertaken. Since the year 1861
science has been in possession of a theory which Maxwell
constructed upon Faraday’s views, and which we therefore call
the Faraday-Maxwell theory. This theory affirms the possibility
of the class of phenomena here discovered just as positively
as the remaining electrical theories are compelled to deny
it. From the outset Maxwell’s theory excelled all others in
elegance and in the abundance of the relations between the
various phenomena which it included.
“The probability of this theory, and therefore the number of
its adherents, increased from year to year. But as long as
Maxwell’s theory depended solely upon the probability of its
results, and not on the certainty of its hypotheses, it could
not completely displace the theories which were opposed to it.
“The fundamental hypotheses of Maxwell’s theory contradicted
the usual views, and did not rest upon the evidence of decisive
experiments. In this connection we can best characterise the
object and the result of our experiments by saying: The object
of these experiments was to test the fundamental hypotheses of
the Faraday-Maxwell theory, and the result of the experiments
is to confirm the fundamental hypotheses of the theory.”
Since Maxwell’s death volumes have been written on electrical
questions, which have all been inspired by his work. The standpoint
from which electrical theory is regarded has been entirely changed. The
greatest masters of mathematical physics have found, in the development
of Maxwell’s views, a task that called for all their powers, and the
harvest of new truths which has been garnered has proved most rich. But
while this is so, the question is still often asked, What is Maxwell’s
theory? Hertz himself concludes the introduction just referred to with
his most interesting answer to this question. Prof. Boltzmann has made
the theory the subject of an important course of lectures. Poincaré,
in the introduction to his “Lectures on Maxwell’s Theories and the
Electro-magnetic Theory of Light,” expresses the difficulty, which many
feel, in understanding what the theory is. “The first time,” he says,
“that a French reader opens Maxwell’s book a feeling of uneasiness,
often even of distrust, is mingled with his admiration. It is only
after prolonged study, and at the cost of many efforts, that this
feeling is dissipated. Some great minds retain it always.” And again
he writes: “A French _savant_, one of those who have most completely
fathomed Maxwell’s meaning, said to me once, ‘I understand everything
in the book except what is meant by a body charged with electricity.’”
In considering this question, Poincaré’s own remark--“Maxwell does
not give a mechanical explanation of electricity and magnetism, he is
only concerned to show that such an explanation is possible”--is most
important.
We cannot find in the “Electricity” an answer to the question--What is
an electric charge? Maxwell did not pretend to know, and the attempt to
give too great definiteness to his views on this point is apt to lead
to a misconception of what those views were.
On the old theories of action at a distance and of electric and
magnetic fluids attracting according to known laws, it was easy to be
mechanical. It was only necessary to investigate the manner in which
such fluids could distribute themselves so as to be in equilibrium,
and to calculate the forces arising from the distribution. The problem
of assigning such a mechanical structure to the ether as will permit
of its exerting the action which occurs in an electro-magnetic field
is a harder one to solve, and till it is solved the question--What is
an electric charge?--must remain unanswered. Still, in order to grasp
Maxwell’s theory this knowledge is not necessary.
The properties of ether in dielectrics and in conductors must be quite
different. In a dielectric the ether has the power of storing energy by
some change in its configuration or its structure; in a conductor this
power is absent, owing probably to the action of the matter of which
the conductor is composed.
When we are said to charge an insulated conductor we really act on the
ether in the neighbourhood of the body so as to store it with energy;
if there be another conductor in the field we cannot store energy in
the ether it contains. As, then, we pass from the outside of this
conductor to its interior there is a sudden change in some mechanical
quantity connected with the ether, and this change shows itself as a
force of attraction between the two conductors. Maxwell called the
change in structure, or in property, which occurs when a dielectric
is thus stored with electrostatic energy, _Electric Displacement_; if
we denote it by D, then the electric force R is equal to 4πD/K, and
hence the energy in a unit of volume is 2πD²/K, where K is a quantity
depending on the insulator.
Now, D, the electric displacement, is a quantity which has direction
as well as magnitude. Its value, therefore, at any point can be
represented by a straight line in the usual way; inside a conductor it
is zero. The total change in D, which takes place all over the surface
of a conductor as we enter it from the outside measures, according
to Maxwell, the total charge on the conductor. At points at which
the lines representing D enter the conductor the charge is negative;
at points at which they leave it the charge is positive; along the
lines of the displacement there exists throughout the ether a tension
measured by 2πD²/K; at right angles to these lines there is a pressure
of the same amount.
In addition to the above the components of the displacement D must
satisfy certain relations which can only be expressed in mathematical
form, the physical meaning of which it is difficult to state in
non-mathematical language.
When these relations are so expressed the problem of finding the value
of the displacement at all points of space becomes determinate, and
the forces acting on the conductors can be obtained. Moreover, the
total change of displacement on entering or leaving a conductor can be
calculated, and this gives the quantity which is known as the total
electrical charge on the conductor. The forces obtained by the above
method are exactly the same as those which would exist if we supposed
each conductor to be charged in the ordinary sense with the quantities
just found, and to attract or repel according to the ordinary laws.
If, then, we define electric displacement as that change which takes
place in a dielectric when it becomes the seat of electrostatic
energy, and if, further, we suppose that the change, whatever it
be mechanically, satisfies certain well-known laws, and that in
consequence certain pressures and tensions exist in the dielectric,
electrostatic problems can be solved without reference to a charge of
electricity residing on the conductors.
Something such as this, it appears to me, is Maxwell’s theory of
electricity as applied to electrostatics. It is not necessary, in order
to understand it, to know what change in the ether constitutes electric
displacement, or what is an electric charge, though, of course, such
knowledge would render our views more definite, and would make the
theory a mechanical one.
When we turn to magnetism and electro-magnetism, Maxwell’s theory
develops itself naturally. Experiment proves that magnetic induction is
connected with the rate of change of electric displacement, according
to the laws already given. If, then, we knew the nature of the change
to which the name “electric displacement” has been given, the nature
of magnetic induction would be known. The difficulties in the way of
any mechanical explanation are, it is true, very great; assuming,
however, that some mechanical conception of “electric displacement”
is possible, Maxwell’s theory gives a consistent account of the other
phenomena of electro-magnetism.
Again, we have, it is true, an electro-magnetic theory of light, but
we do not know the nature of the change in the ether which affects
our eyes with the sensation of light. Is it the same as electric
displacement, or as magnetic induction, or since, when electric
displacement is varying, magnetic induction always accompanies it, is
the sensation of light due to the combined effect of the two?
These questions remain unanswered. It may be that light is neither
electric displacement nor magnetic induction, but some quite different
periodic change of structure of the ether, which travels through the
ether at the same rate as these quantities, and obeys many of the same
laws.
In this respect there is a material difference between the ordinary
theory of light and the electro-magnetic theory. The former is a
mechanical theory; it starts from the assumption that the periodic
change which constitutes light is the ordinary linear displacement of a
medium--the ether--having certain mechanical properties, and from those
properties it deduces the laws of optics with more or less success.
Lord Kelvin, in his labile ether, has devised a medium which could
exist and which has the necessary mechanical properties. The periodic
linear displacements of the labile ether would obey the laws of
light, and from the fundamental hypotheses of the theory, a mechanical
explanation, reasonably satisfactory in its main features, can be given
of most purely optical phenomena. The relations between light and
electricity, or light and magnetism, are not, however, touched by this
theory; indeed, they cannot be touched without making some assumption
as to what electric displacement is.
In recent years various suggestions have been made as to the nature
of the change which constitutes electric displacement. One theory,
due to Von Helmholtz, supposes that the electro-kinetic momentum, or
vector potential of Maxwell, is actually the momentum of the moving
ether; according to another, suggested, it would appear originally
in a crude form by Challis, and developed within the last few months
in very satisfactory detail by Larmor, the velocity of the ether is
magnetic force; others have been devised, but we are still waiting for
a second Newton to give us a theory of the ether which shall include
the facts of electricity and magnetism, luminous radiation, and it may
be gravitation.[71]
Meanwhile we believe that Maxwell has taken the first steps towards
this discovery, and has pointed out the lines along which the future
discoverer must direct his search, and hence we claim for him a
foremost place among the leaders of this century of science.
FOOTNOTES
[1] A full biographical account of the Clerk and Maxwell families is
given in a note by Miss Isabella Clerk in the “Life of James Clerk
Maxwell,” and from this the above brief statement has been taken.
[2] “Life of J. C. Maxwell,” p. 26.
[3] “Life of J. C. Maxwell,” p. 27.
[4] “Life of J. C. Maxwell,” p. 49.
[5] “Life of J. C. Maxwell,” p. 52.
[6] “Life of J. C. Maxwell,” p. 56.
[7] “Life of J. C. Maxwell,” p. 67.
[8] “Life of J. C. Maxwell,” p. 75.
[9] Professor Garnett in _Nature_, November 13th, 1879.
[10] “Life of J. C. Maxwell,” p. 105.
[11] “Life of J. C. Maxwell,” p. 116.
[12] “Life of J. C. Maxwell,” pp. 123–129.
[13] “Life of J. C. Maxwell,” p. 190.
[14] Dean of Canterbury.
[15] Master of Trinity.
[16] “Life of J. C. Maxwell,” p. 174.
[17] “Life of J. C. Maxwell,” p. 195.
[18] “Life of J. C. Maxwell,” p. 207.
[19] “Life of J. C. Maxwell,” p. 208.
[20] “Life of J. C. Maxwell,” p. 210.
[21] “Life of J. C. Maxwell,” p. 211.
[22] “Life of J. C. Maxwell,” p. 216.
[23] “Life of J. C. Maxwell,” p. 256.
[24] “Life of J. C. Maxwell,” p. 267.
[25] “Life of J. C. Maxwell,” p. 269.
[26] “Life of J. C. Maxwell,” p. 278.
[27] “Life of J. C. Maxwell,” p. 292.
[28] “Life of J. C. Maxwell,” p. 303.
[29] “Life of J. C. Maxwell,” p. 259.
[30] B.A. Report, Newcastle, 1863.
[31] “Life of J. C. Maxwell,” p. 340.
[32] “Life of J. C. Maxwell,” p. 332.
[33] “Life of J. C. Maxwell,” p. 336.
[34] The Professors who were consulted were Challis, Willis, Stokes,
Cayley, Adams, and Liveing.
[35] “Life of J. C. Maxwell,” p. 349.
[36] “Life of J. C. Maxwell,” p. 381.
[37] “Life of J. C. Maxwell,” p. 379.
[38] An account of the laboratory is given in _Nature_, vol. x., p. 139.
[39] The Chancellor continued to take to the end of his life a warm
interest in the work at the laboratory. In 1887, the Jubilee year, as
Proctor--at the same time I held the office of Demonstrator--it was
my duty to accompany the Chancellor and other officers to Windsor to
present an address from the University to Her Majesty. I was introduced
to the Chancellor at Paddington, and he at once began to question me
closely about the progress of the laboratory, the number of students,
and the work being done there, showing himself fully acquainted with
recent progress.
[40] In 1894 the list contained, in Part II., sixteen names, and in
Part I., one hundred and three names.
[41] Under the new regulations Physics was removed from the first part
of the Tripos and formed, with the more advanced parts of Astronomy
and Pure Mathematics, a part by itself, to which only the Wranglers
were admitted. Thus the number of men encouraged to read Physics was
very limited. This pernicious system was altered in the regulations
at present in force, which came into action in 1892. Part I. of the
Mathematical Tripos now contains Heat, Elementary Hydrodynamics
and Sound, and the simpler parts of Electricity and Magnetism, and
candidates for this examination do come to the laboratory, though not
in very large numbers. The more advanced parts both of Mathematics and
Physics are included in Part II.
[42] “Life of J. C. Maxwell,” p. 383.
[43] “Statique Expérimentale et Théorique des Liquides soumis aux
seules Forces Moléculaires.” Par J. Plateau, Professeur à l’Université
de Gaud.
[44] The “Red Lions” are a club formed by Members of the British
Association to meet for relaxation after the graver labours of the day.
[45] “Leonum arida nutrix.”--_Horace._
[46] _v.r._, endless.
[47] “Life of J. C. Maxwell,” p. 394.
[48] “Life of J. C. Maxwell,” p. 404.
[49] In his “Hydrodynamics,” published in 1738, Daniel Bernouilli
had discussed the constitution of a gas, and had proved from general
considerations that the pressure, if it arose from the impact of a
number of moving particles, must be proportional to the square of their
velocity. (_See_ “Pogg. Ann.,” Bd. 107, 1859, p. 490.)
[50] The proof is as follows:--
If σ be the specific heat at constant volume, σ′ at constant pressure,
and consider a unit of mass of gas at pressure p and volume v, let the
volume increase by an amount dv, while the temperature dy.
Thus σ′dT = σdT + pdv
But pv = ⅔T/m
Hence p being constant,
pdv = ⅔ dT/m
Therefore σ′ = σ + ⅔ 1/m
Now suppose an amount of heat, dH, is given to a single molecule and
that its temperature is T. Its specific heat is σ, and
dH = σmdT
But dH = βdT
Therefore β = σm
Hence 1/m = σ/β
Thus σ′ = σ(1 + 2/(3β))
And σ′/σ = γ
Therefore γ = 1 + 2/(3β)
Or β = 2/(3(γ-1))
[51] Owing to an error of calculation the actual value obtained by
Maxwell from these observations for the coefficient of viscosity is too
great. More recent observers have found lower values than those given
by him; the difference is thus explained.
[52] Studien über das Gleichgewicht der lebendigen Kraft zwischen
bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII., 1868.
[53] Another supposition which might be made, and which is necessary
in order to explain various actions observed in a compound gas under
electric force, is that the parts of which a molecule is composed are
continually changing. Thus a molecule of steam consists of two parts of
hydrogen, one of oxygen, but a given molecule of oxygen is not always
combined with the same two molecules of hydrogen; the particles are
continually changed. In Maxwell’s paper an hypothesis of this kind is
not dealt with.
[54] _Nature_, vol. 1., p. 152 (December 13th, 1894).
[55] See papers by Mr. Capstick, _Phil. Trans._, vols. 185–186.
[56] _Nature_, vol. x.
[57] An historical account of the development of the science of
electricity will be found in the article “Electricity” in the
_Encyclopædia Britannica_, ninth edition, by Professor Chrystal.
[58] Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,”
p. 15.
[59] J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on
Electrical Theories.
[60] Papers on “Electrostatics,” etc., p. 26.
[61] It is difficult to explain without analysis exactly what is
measured by Maxwell’s Vector Potential. Its rate of change at any
point of space measures the electromotive force at that point, so far
as it is due to variations of the electric current in neighbouring
conductors; the magnetic induction depends on the first differential
coefficients of the components of the electro-tonic state; the
electric current is related to their second differential coefficients
in the same manner as the density of attracting matter is related
to the potential it produces. In language which is now frequently
used in mathematical physics, the electromotive force at a point
due to magnetic induction is proportioned to the rate of change of
the Vector Potential, the magnetic induction depends on the “curl”
of the Vector Potential, while the electric current is measured by
the “concentration” of the Vector Potential. From a knowledge of the
Vector Potential these other quantities can be obtained by processes of
differentiation.
[62] The 4 π is introduced because of the system of units usually
employed to measure electrical quantities. If we adopted Mr. Oliver
Heaviside’s “rational units,” it would disappear, as it does in (B).
[63] For an exact statement as to the relation between the directions
of the lines of electric displacement and of the magnetic force,
reference must be made to Professor Poynting’s paper, _Phil. Trans._,
1885, Part II., pp. 280, 281. The ideas are further developed in a
series of articles in the _Electrician_, September, 1895. Reference
should also be made to J. J. Thomson’s “Recent Researches in
Electricity and Magnetism.”
[64] Preface to Newton’s “Principia,” 2nd edition.
[65] “Lezioni Accademiche” (Firenze, 1715), p. 25.
[66] In his sentence μ stands for the refractive index.
[67] Hertz’s papers have been translated into English by D. E. Jones,
and are published under the title of _Electric Waves_.
[68] Some of the consequences of this electrical resonance have been
very strikingly shown by Professor Oliver Lodge. _See_ _Nature_,
February 20th, 1890.
[69] Hertz’s original results were no doubt affected by waves reflected
from the walls and floor of the room in which he worked. An iron
stove also, which was near his apparatus, may have had a disturbing
influence; but for all this, it is to his genius and his brilliant
achievements that the complete establishment of Maxwell’s theory is due.
[70] The analogy does not consist only in the agreement between the
more or less accurately measured velocities. The approximately equal
velocity is only one element among many others.
[71] For a very suggestive account of some possible theories,
reference should be made to the presidential address of Professor W. M.
Hicks to Section A of the British Association at Ipswich in 1895.
INDEX.
Aberdeen, Maxwell elected Professor at, 45;
formation of University of, 51
Adams, W. G., succeeds Maxwell as Professor at King’s College,
London, 58
Adams Prize, The, 48;
gained by Maxwell, 50
Ampère, 155, 204
Ampère’s Law, 155, 156
_Annals of Philosophy_, Thomson’s, 112, 113
“Apostles,” club so called, 30, 89
Arago, 157
Aragonite, 200
Atom, article by Maxwell in _Encyclopædia Britannica_, 108
Avogadros’ Law, 117, 124
Bakerian Lecture, delivered by Maxwell, 58
Berkeley on the Theory of Vision, 38
Bernouilli, D., 113
Blackburne, Professor, 16
Blore, Rev. E. W., 67
Boehm, Bust of Maxwell by, 90
Boltzmann, Dr., 135, 137, 138, 144, 216
Boltzmann-Maxwell Theory, The, 140, 145
Boscovitch on Atoms, 108, 109
Boyle’s Law, 114, 117, 124
Brewster, Sir David, on Colour Sensation, 99
British Association, Maxwell and, 42,54;
Lecture before, 80–82;
Lines on President’s address, 83, 84
Butler, Dr. H. M., extract from sermon on Maxwell, 32–35
Bryan, G. H., 141, 143
Cambridge, Maxwell at, 28–46;
Mathematical Tripos at, 60;
Foundation of Professorship of Experimental Physics at, 66
_Cambridge and Dublin Mathematical Journal_, Papers by Maxwell in, 30
Campbell, Professor L., 9, 10, 12, 14, 22, 52, 57, 79
Cauchy’s Formula, 208
Cavendish, Henry, 73, 74;
Works of, edited by Maxwell, 87, 154, 155
Cavendish Laboratory, built and presented to University of
Cambridge, 73, 74
Cay, Miss Frances, 11
Cayley Portrait Fund, lines to Committee, 86
Challis, Professor, 49
Charles’ Law, 124
Chemical Society, Maxwell’s lecture before, 80–82
Clausius, on kinetic theory of gases, 119, 129, 130, 137
Clerks of Penicuik, The, 9, 10
Colour Perception, 94
Colour Sensation, Young on, 97, 98;
Sir D. Brewster on, 99
Colours, paper by Maxwell, on, 40, 41;
Helmholtz on, 99
Conductors and Insulators, Distinction between, 173
Cookson, Dr., 61
Corsock, Maxwell buried at, 90
Cotes, 202
Coulomb, 154
Curves, investigated by Maxwell, 19
Daniell’s cells, 77
Democritus, 108
Demonstrator of Physics, W. Garnett appointed, 75
Description of Oval Curves, first paper by Maxwell, 19
Devonshire, Duke of, Cavendish Laboratory built by, 73, 74;
Letter of Thanks from University of Cambridge, 74
Dewar, Miss K. M., her marriage to Maxwell, 51
Dickinson, Lowes; Portrait of Maxwell by, 90
Diffusion of gases, 128
Discs for colour experiments, 99–101
Droop, H. R., 57
Dynamical Theory of the Electro-magnetic Field, Maxwell on, 57, 177
Dynamical Theory of Gases, Maxwell on, 58, 134
Edinburgh Academy, Maxwell’s school-life at, 13–18
Edinburgh, Royal Society of, Maxwell at meetings of, 18
Edinburgh, University of, Maxwell at, 22
Elastic Spheres, 144
Electric Displacement, 218, 219, 220
Electrical Theories, 94, 154, 155
Electricity and Magnetism, Maxwell’s book on, 59, 77, 79, 147, 155,
156, 176, 180–201;
papers by Lord Kelvin on, 161–2;
Application of Mathematical Analysis to, paper by G. Green, 158
Electricity, Modern Views of, by Professor Lodge, 177
Electro-kinetic Momentum, 221
Electro-magnetic Field, Dynamical Theory of, Maxwell on, 57, 177
Electro-magnetic Induction, 157
Electro-magnetic Theory of Light, 174
Electro-tonic State, 164
Electrostatic Induction, Faraday on, 159
_Encyclopædia Britannica_, articles by Maxwell in, 80, 108, 146
Ether, labile, 220
Experimental Physics, foundation of Professorship at Cambridge, 66;
Election of Maxwell, 68
Faraday on electrical science, 157;
on electrostatic induction, 159
Faraday’s Lines of Force, paper by Maxwell on, 44, 45, 148–153
Fawcett, W. M., architect of Cavendish Laboratory, 73
Fitzgerald, Professor, 177, 211
Forbes, Professor J. D., 18, 44, 54;
friendship with Maxwell, 19;
paper on Theory of Glaciers, 19;
resigns Professorship at Edinburgh, 54
Galvani, 155
Garnett, W., appointed Demonstrator of Physics at Cambridge, 75;
Life of Maxwell by, 94
Gases, Molecular theory of, 57, 108;
Waterston on general theory of, 118;
Clausius on, 119;
diffusion of, 128
Gauss’ Theory, 156
Gay Lussac’s Law, 117
General Theory of Gases, Waterston on, 118;
Clausius on, 119
Glenlair, home of Maxwell, 11, 23;
laboratory at, 24;
Maxwell’s life at, 58, 59;
“Electricity and Magnetism” written at, 79
Gordon, J. E. H., 77, 78
Green, G., of Nottingham, paper on electricity and magnetism, 158;
inventor of term “Potential,” 158
Hamilton, Sir W. R., 22
Hamilton’s Principle, 190
Heat, Text-book on, by Maxwell, 79
Helmholtz, 99, 156, 157, 175, 221
Henry, J., of Washington, on electro-magnetic induction, 157
Herapath on molecules, 112–116
Hertz, Heinrich, 204, 209–213
Hicks, W. M., 221
Hockin, C., 56
Holman, Professor, 133
Iceland Spar, 200
Insulators and Conductors, Distinction between, 173
Jenkin, Fleeming, 55, 56
Kelland, Professor, 22
Kelvin, Lord, 16, 142, 158, 159, 160, 168;
on the Uniform Motion of Heat, 160;
papers on Electricity and Magnetism, 161, 162
Kinetic energy, 124, 129, 136, 139, 191
King’s College, London, Maxwell elected Professor at, 54
Kohlrausch, 206
Kundt, 132
Labile Ether, 220
Laboratory at Glenlair, 24
Lagrange, 179
Lagrange’s Equations, 179, 190
Laplace, 155
Larmor, J., 141, 142
Lecher, 214
Lenz, 157
Litchfield, R. B., 46
Light, Electro-magnetic Theory of, 174;
Waves of, 198, 199
Lodge, Professor, book on Modern Views of Electricity, 177
Lucretius, 108
Luminous Radiation, 221
Mathematical Tripos at Cambridge, subjects, 60;
Maxwell an examiner for, 60, 80;
experimental work in, 76
Matter and Motion, Maxwell on, 79
Maxwell, James Clerk, parentage and birthplace, 10, 11;
childhood and school-days, 12–18;
his mother’s death, 13;
first lessons in geometry, 17;
attends meetings of Royal Society of Edinburgh, 18;
his first published paper, 19;
friendship with Professor Forbes, 19;
his polariscope, 20;
enters the University of Edinburgh, 22;
papers on Rolling Curves and Elastic Solids, 23;
vacations at Glenlair, 23;
laboratory at Glenlair, 24;
undergraduate life at Cambridge, 28–36;
elected scholar of Trinity, 29;
illness at Lowestoft, 29;
his friends at Cambridge, 30;
Tripos and degree, 35–37;
early researches, 38–44;
paper on Colours, 40, 41;
elected Fellow of Trinity, 43;
Lecturer at Trinity, 43;
Professor at Aberdeen, 45;
his father’s death, 45;
gains the Adams Prize, 50;
marriage, 51;
powers as teacher and lecturer, 52, 53;
Professor at King’s College, London, 54;
gains the Rumford Medal, 55;
delivers Bakerian lecture, 58;
resigns Professorship at King’s College, London, 58;
life at Glenlair, 58, 59;
visit to Italy, 59;
Examiner for Mathematical Tripos, 60, 80;
elected Professor of Experimental Physics at Cambridge, 68;
Introductory Lecture, 68–72;
Examiner for Natural Sciences Tripos, 79;
articles in _Encyclopædia Britannica_, 80, 118, 146;
papers in Nature, 80;
lectures before British Association and Chemical Society, 80–82;
humorous poems, 83–87;
delivers Rede Lecture on the Telephone, 89;
last illness and death, 89, 90;
buried at Corsock, 90;
bust and portrait, 90;
religious views, 91, 92
Maxwell, John Clerk, 10, 11
Meyer, O. E., 133
Mill’s Logic, 38
Molecular Evolution, Lines on, 85
---- Physics, 94
---- Constitution of Bodies, Maxwell on, 146
---- Theory of Gases, 57, 108
Molecules, 109, 110;
Herapath on, 112–116;
lecture by Maxwell on, 146
Motion of Saturn’s Rings, subject for Adams Prize, 49
Munro, J. C., 40, 56, 68, 82
Natural Sciences Tripos, Maxwell Examiner for, 79
_Nature_, papers by Maxwell in, 80
Neumann, F. E., 156, 157
Newton’s Lunar Theory and Astronomy, 50
---- Principia, 202
Nicol, Wm., inventor of the polarising prism, 20
Niven, W. D., 27, 46, 51, 52, 60, 78, 87, 88, 93
Obermeyer, 134
Ohm’s Law, 77
Ophthalmoscope devised by Maxwell, 83
Oval Curves, Description of, Maxwell’s first paper, 19
Parkinson, Dr., 49
_Philosophical Magazine_, 56, 99, 115, 120, 133, 142
_Philosophical Transactions_, 56, 89, 132, 145
Physical Lines of Force, Maxwell on, 56, 158
Physics, Instruction in, at Cambridge, 61;
Report of Syndicate on, 62–64;
Demonstrator appointed, 75
Poincaré, 216
Poisson, 44;
on distribution of electricity, 155
Polariscope, made by Maxwell, 20
“Potential,” term invented by G. Green, 158;
the Vector, 165, 221
Poynting, Professor, 187–189
Puluj, 134
Quincke, 206
Radiation, Luminous, 221
Rarefied Gases, Stresses in, paper by Maxwell, 135, 145
Rayleigh, Lord, 67, 77
Rede Lecture on the Telephone, delivered by Maxwell, 89
Report on Electrical Theories, J. J. Thomson, 204
---- of Syndicate as to instruction in Physics at Cambridge, 62–64
Robertson, C. H., 28
Rolling Curves, Maxwell on, 23
Royal Society, The, Maxwell and, 55;
Transactions of, 89
Rumford Medal gained by Maxwell, 55, 106
Sabine, Major-General, Vice-President of Royal Society, 106
Smith’s Prizes, 36
Standards of Electrical Resistance, Committee on, 55
Stewart, Balfour, 56, 125
Stresses in Rarefied Gases, Maxwell on, 135, 155
Tait, Professor P. G., 21, 26, 94
Tayler, Rev. C. B., 29
Telephone, Rede Lecture by Maxwell on, 89
Theory of Glaciers, Prof. Forbes on, 19
Thomson, J. J., 157, 208;
Report on Electrical Theories, 205
Thomson’s _Annals of Philosophy_, 112, 113
Uniform Motion of Heat in Homogeneous Solid Bodies, paper by Lord
Kelvin, 160, 161
University Commission, 47, 48, 62
Urr, Vale of, 11
Vector Potential, The, 165, 221
Viscosity of Gases, Experiments on, 58, 125, 132
Volta, Inventor of voltaic pile, 155
Waterston, J. J., on molecular theory of gases, 114, 115;
on general theory of gases, 118
Waves of Light, 198, 199
Weber, W., 156, 206
Wedderburn, Mrs., 14
Wheatstone’s Bridge, 77
Williams, J., Archdeacon of Cardigan, 16
Willis, Professor, 44
Wilson, E., lines in memory of, 86, 87
Young, T., on colour sensation, 97, 98
PRINTED BY CASSELL & COMPANY, LIMITED, LA BELLE SAUVAGE, LONDON, E.C.
* * * * * *
Transcriber’s note:
Punctuation, hyphenation, and spelling were made consistent when a
predominant preference was found in the original book; otherwise they
were not changed.
Simple typographical errors were corrected; unpaired quotation
marks were remedied when the change was obvious, and otherwise left
unpaired.
Illustrations in this eBook have been positioned between paragraphs
and outside quotations.
Footnotes, originally at the bottoms of pages, have been collected,
renumbered, and placed just before the Index.
The Index was not checked for proper alphabetization or correct page
references.
Some values in the original book are known today to be incorrect, but
have not been changed here.
Page 133: The last equation on the page,
μ = μ₀ (1 + .00275 t - .00000034 t²)
was misprinted as
μ = μ₀ {1 + .00275 t .00000034 t²}.
It is shown here with corrections based on its cited source:
https://archive.org/details/s05philosophicalmag21londuoft/page/212
Page 144: “possibly of ether atoms bound with them” was printed that
way, but “ether” may be a misprint for “other”.
Page 170: “hence at C, where they touch” was printed as “A”, but Figure
1 at that point is labelled “C”.