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James Clerk Maxwell >> Five of Maxwell\'s Papers
The mutual action and reaction between the different departments of
human thought is so interesting to the student of scientific progress,
that, at the risk of still further encroaching on the valuable time of
the Section, I shall say a few words on a branch of physics which not
very long ago would have been considered rather a branch of
metaphysics. I mean the atomic theory, or, as it is now called, the
molecular theory of the constitution of bodies.
Not many years ago if we had been asked in what regions of physical
science the advance of discovery was least apparent, we should have
pointed to the hopelessly distant fixed stars on the one hand, and to
the inscrutable delicacy of the texture of material bodies on the
other.
Indeed, if we are to regard Comte as in any degree representing the
scientific opinion of his time, the research into what takes place
beyond our own solar system seemed then to be exceedingly unpromising,
if not altogether illusory.
The opinion that the bodies which we see and handle, which we can set
in motion or leave at rest, which we can break in pieces and destroy,
are composed of smaller bodies which we cannot see or handle, which
are always in motion, and which can neither be stopped nor broken in
pieces, nor in any way destroyed or deprived of the least of their
properties, was known by the name of the Atomic theory. It was
associated with the names of Democritus, Epicurus, and Lucretius, and
was commonly supposed to admit the existence only of atoms and void,
to the exclusion of any other basis of things from the universe.
In many physical reasonings and mathematical calculations we are
accustomed to argue as if such substances as air, water, or metal,
which appear to our senses uniform and continuous, were strictly and
mathematically uniform and continuous.
We know that we can divide a pint of water into many millions of
portions, each of which is as fully endowed with all the properties of
water as the whole pint was; and it seems only natural to conclude
that we might go on subdividing the water for ever, just as we can
never come to a limit in subdividing the space in which it is
contained. We have heard how Faraday divided a grain of gold into an
inconceivable number of separate particles, and we may see Dr Tyndall
produce from a mere suspicion of nitrite of butyle an immense cloud,
the minute visible portion of which is still cloud, and therefore must
contain many molecules of nitrite of butyle.
But evidence from different and independent sources is now crowding in
upon us which compels us to admit that if we could push the process of
subdivision still further we should come to a limit, because each
portion would then contain only one molecule, an individual body, one
and indivisible, unalterable by any power in nature.
Even in our ordinary experiments on very finely divided matter we find
that the substance is beginning to lose the properties which it
exhibits when in a large mass, and that effects depending on the
individual action of molecules are beginning to become prominent.
The study of these phenomena is at present the path which leads to the
development of molecular science.
That superficial tension of liquids which is called capillary
attraction is one of these phenomena. Another important class of
phenomena are those which are due to that motion of agitation by which
the molecules of a liquid or gas are continually working their way
from one place to another, and continually changing their course, like
people hustled in a crowd.
On this depends the rate of diffusion of gases and liquids through
each other, to the study of which, as one of the keys of molecular
science, that unwearied inquirer into nature's secrets, the late Prof.
Graham, devoted such arduous labour.
The rate of electrolytic conduction is, according to Wiedemann's
theory, influenced by the same cause; and the conduction of heat in
fluids depends probably on the same kind of action. In the case of
gases, a molecular theory has been developed by Clausius and others,
capable of mathematical treatment, and subjected to experimental
investigation; and by this theory nearly every known mechanical
property of gases has been explained on dynamical principles; so that
the properties of individual gaseous molecules are in a fair way to
become objects of scientific research.
Now Mr Stoney has pointed out[1] that the numerical results of
experiments on gases render it probable that the mean distance of
their particles at the ordinary temperature and pressure is a quantity
of the same order of magnitude as a millionth of a millimetre, and Sir
William Thomson has since[2] shewn, by several independent lines of
argument, drawn from phenomena so different in themselves as the
electrification of metals by contact, the tension of soap-bubbles, and
the friction of air, that in ordinary solids and liquids the average
distance between contiguous molecules is less than the
hundred-millionth, and greater than the two-thousand-millionth of a
centimetre.
[1] _Phil. Mag._, Aug. 1868.
[2] _Nature_, March 31, 1870.
These, of course, are exceedingly rough estimates, for they are
derived from measurements some of which are still confessedly very
rough; but if at the present time, we can form even a rough plan for
arriving at results of this kind, we may hope that, as our means of
experimental inquiry become more accurate and more varied, our
conception of a molecule will become more definite, so that we may be
able at no distant period to estimate its weight with a greater degree
of precision.
A theory, which Sir W. Thomson has founded on Helmholtz's splendid
hydrodynamical theorems, seeks for the properties of molecules in the
ring vortices of a uniform, frictionless, incompressible fluid. Such
whirling rings may be seen when an experienced smoker sends out a
dexterous puff of smoke into the still air, but a more evanescent
phenomenon it is difficult to conceive. This evanescence is owing to
the viscosity of the air; but Helmholtz has shewn that in a perfect
fluid such a whirling ring, if once generated, would go on whirling
for ever, would always consist of the very same portion of the fluid
which was first set whirling, and could never be cut in two by any
natural cause. The generation of a ring-vortex is of course equally
beyond the power of natural causes, but once generated, it has the
properties of individuality, permanence in quantity, and
indestructibility. It is also the recipient of impulse and of energy,
which is all we can affirm of matter; and these ring-vortices are
capable of such varied connexions and knotted self-involutions, that
the properties of differently knotted vortices must be as different as
those of different kinds of molecules can be.
If a theory of this kind should be found, after conquering the
enormous mathematical difficulties of the subject, to represent in any
degree the actual properties of molecules, it will stand in a very
different scientific position from those theories of molecular action
which are formed by investing the molecule with an arbitrary system of
central forces invented expressly to account for the observed
phenomena.
In the vortex theory we have nothing arbitrary, no central forces or
occult properties of any other kind. We have nothing but matter and
motion, and when the vortex is once started its properties are all
determined from the original impetus, and no further assumptions are
possible.
Even in the present undeveloped state of the theory, the contemplation
of the individuality and indestructibility of a ring-vortex in a
perfect fluid cannot fail to disturb the commonly received opinion
that a molecule, in order to be permanent, must be a very hard body.
In fact one of the first conditions which a molecule must fulfil is,
apparently, inconsistent with its being a single hard body. We know
from those spectroscopic researches which have thrown so much light on
different branches of science, that a molecule can be set into a state
of internal vibration, in which it gives off to the surrounding medium
light of definite refrangibility--light, that is, of definite
wave-length and definite period of vibration. The fact that all the
molecules (say, of hydrogen) which we can procure for our experiments,
when agitated by heat or by the passage of an electric spark, vibrate
precisely in the same periodic time, or, to speak more accurately,
that their vibrations are composed of a system of simple vibrations
having always the same periods, is a very remarkable fact.
I must leave it to others to describe the progress of that splendid
series of spectroscopic discoveries by which the chemistry of the
heavenly bodies has been brought within the range of human inquiry. I
wish rather to direct your attention to the fact that, not only has
every molecule of terrestrial hydrogen the same system of periods of
free vibration, but that the spectroscopic examination of the light of
the sun and stars shews that, in regions the distance of which we can
only feebly imagine, there are molecules vibrating in as exact unison
with the molecules of terrestrial hydrogen as two tuning-forks tuned
to concert pitch, or two watches regulated to solar time.
Now this absolute equality in the magnitude of quantities, occurring
in all parts of the universe, is worth our consideration.
The dimensions of individual natural bodies are either quite
indeterminate, as in the case of planets, stones, trees, &c., or they
vary within moderate limits, as in the case of seeds, eggs, &c.; but
even in these cases small quantitative differences are met with which
do not interfere with the essential properties of the body.
Even crystals, which are so definite in geometrical form, are variable
with respect to their absolute dimensions.
Among the works of man we sometimes find a certain degree of
uniformity.
There is a uniformity among the different bullets which are cast in
the same mould, and the different copies of a book printed from the
same type.
If we examine the coins, or the weights and measures, of a civilized
country, we find a uniformity, which is produced by careful adjustment
to standards made and provided by the state. The degree of uniformity
of these national standards is a measure of that spirit of justice in
the nation which has enacted laws to regulate them and appointed
officers to test them.
This subject is one in which we, as a scientific body, take a warm
interest; and you are all aware of the vast amount of scientific work
which has been expended, and profitably expended, in providing weights
and measures for commercial and scientific purposes.
The earth has been measured as a basis for a permanent standard of
length, and every property of metals has been investigated to guard
against any alteration of the material standards when made. To weigh
or measure any thing with modern accuracy, requires a course of
experiment and calculation in which almost every branch of physics and
mathematics is brought into requisition.
Yet, after all, the dimensions of our earth and its time of rotation,
though, relatively to our present means of comparison, very permanent,
are not so by any physical necessity. The earth might contract by
cooling, or it might be enlarged by a layer of meteorites falling on
it, or its rate of revolution might slowly slacken, and yet it would
continue to be as much a planet as before.
But a molecule, say of hydrogen, if either its mass or its time of
vibration were to be altered in the least, would no longer be a
molecule of hydrogen.
If, then, we wish to obtain standards of length, time, and mass which
shall be absolutely permanent, we must seek them not in the
dimensions, or the motion, or the mass of our planet, but in the
wave-length, the period of vibration, and the absolute mass of these
imperishable and unalterable and perfectly similar molecules.
When we find that here, and in the starry heavens, there are
innumerable multitudes of little bodies of exactly the same mass, so
many, and no more, to the grain, and vibrating in exactly the same
time, so many times, and no more, in a second, and when we reflect
that no power in nature can now alter in the least either the mass or
the period of any one of them, we seem to have advanced along the path
of natural knowledge to one of those points at which we must accept
the guidance of that faith by which we understand that "that which is
seen was not made of things which do appear."
One of the most remarkable results of the progress of molecular
science is the light it has thrown on the nature of irreversible
processes--processes, that is, which always tend towards and never
away from a certain limiting state. Thus, if two gases be put into
the same vessel, they become mixed, and the mixture tends continually
to become more uniform. If two unequally heated portions of the same
gas are put into the vessel, something of the kind takes place, and
the whole tends to become of the same temperature. If two unequally
heated solid bodies be placed in contact, a continual approximation of
both to an intermediate temperature takes place.
In the case of the two gases, a separation may be effected by chemical
means; but in the other two cases the former state of things cannot be
restored by any natural process.
In the case of the conduction or diffusion of heat the process is not
only irreversible, but it involves the irreversible diminution of that
part of the whole stock of thermal energy which is capable of being
converted into mechanical work.
This is Thomson's theory of the irreversible dissipation of energy,
and it is equivalent to the doctrine of Clausius concerning the growth
of what he calls Entropy.
The irreversible character of this process is strikingly embodied in
Fourier's theory of the conduction of heat, where the formulae
themselves indicate, for all positive values of the time, a possible
solution which continually tends to the form of a uniform diffusion of
heat.
But if we attempt to ascend the stream of time by giving to its symbol
continually diminishing values, we are led up to a state of things in
which the formula has what is called a critical value; and if we
inquire into the state of things the instant before, we find that the
formula becomes absurd.
We thus arrive at the conception of a state of things which cannot be
conceived as the physical result of a previous state of things, and we
find that this critical condition actually existed at an epoch not in
the utmost depths of a past eternity, but separated from the present
time by a finite interval.
This idea of a beginning is one which the physical researches of
recent times have brought home to us, more than any observer of the
course of scientific thought in former times would have had reason to
expect.
But the mind of man is not, like Fourier's heated body, continually
settling down into an ultimate state of quiet uniformity, the
character of which we can already predict; it is rather like a tree,
shooting out branches which adapt themselves to the new aspects of the
sky towards which they climb, and roots which contort themselves among
the strange strata of the earth into which they delve. To us who
breathe only the spirit of our own age, and know only the
characteristics of contemporary thought, it is as impossible to
predict the general tone of the science of the future as it is to
anticipate the particular discoveries which it will make.
Physical research is continually revealing to us new features of
natural processes, and we are thus compelled to search for new forms
of thought appropriate to these features. Hence the importance of a
careful study of those relations between mathematics and Physics which
determine the conditions under which the ideas derived from one
department of physics may be safely used in forming ideas to be
employed in a new department.
The figure of speech or of thought by which we transfer the language
and ideas of a familiar science to one with which we are less
acquainted may be called Scientific Metaphor.
Thus the words Velocity, Momentum, Force, &c. have acquired certain
precise meanings in Elementary Dynamics. They are also employed in
the Dynamics of a Connected System in a sense which, though perfectly
analogous to the elementary sense, is wider and more general.
These generalized forms of elementary ideas may be called metaphorical
terms in the sense in which every abstract term is metaphorical. The
characteristic of a truly scientific system of metaphors is that each
term in its metaphorical use retains all the formal relations to the
other terms of the system which it had in its original use. The
method is then truly scientific--that is, not only a legitimate
product of science, but capable of generating science in its turn.
There are certain electrical phenomena, again, which are connected
together by relations of the same form as those which connect
dynamical phenomena. To apply to these the phrases of dynamics with
proper distinctions and provisional reservations is an example of a
metaphor of a bolder kind; but it is a legitimate metaphor if it
conveys a true idea of the electrical relations to those who have been
already trained in dynamics.
Suppose, then, that we have successfully introduced certain ideas
belonging to an elementary science by applying them metaphorically to
some new class of phenomena. It becomes an important philosophical
question to determine in what degree the applicability of the old
ideas to the new subject may be taken as evidence that the new
phenomena are physically similar to the old.
The best instances for the determination of this question are those in
which two different explanations have been given of the same thing.
The most celebrated case of this kind is that of the corpuscular and
the undulatory theories of light. Up to a certain point the phenomena
of light are equally well explained by both; beyond this point, one of
them fails.
To understand the true relation of these theories in that part of the
field where they seem equally applicable we must look at them in the
light which Hamilton has thrown upon them by his discovery that to
every brachistochrone problem there corresponds a problem of free
motion, involving different velocities and times, but resulting in the
same geometrical path. Professor Tait has written a very interesting
paper on this subject.
According to a theory of electricity which is making great progress in
Germany, two electrical particles act on one another directly at a
distance, but with a force which, according to Weber, depends on their
relative velocity, and according to a theory hinted at by Gauss, and
developed by Riemann, Lorenz, and Neumann, acts not instantaneously,
but after a time depending on the distance. The power with which this
theory, in the hands of these eminent men, explains every kind of
electrical phenomena must be studied in order to be appreciated.
Another theory of electricity, which I prefer, denies action at a
distance and attributes electric action to tensions and pressures in
an all-pervading medium, these stresses being the same in kind with
those familiar to engineers, and the medium being identical with that
in which light is supposed to be propagated.
Both these theories are found to explain not only the phenomena by the
aid of which they were originally constructed, but other phenomena,
which were not thought of or perhaps not known at the time; and both
have independently arrived at the same numerical result, which gives
the absolute velocity of light in terms of electrical quantities.
That theories apparently so fundamentally opposed should have so large
a field of truth common to both is a fact the philosophical importance
of which we cannot fully appreciate till we have reached a scientific
altitude from which the true relation between hypotheses so different
can be seen.
I shall only make one more remark on the relation between Mathematics
and Physics. In themselves, one is an operation of the mind, the
other is a dance of molecules. The molecules have laws of their own,
some of which we select as most intelligible to us and most amenable
to our calculation. We form a theory from these partial data, and we
ascribe any deviation of the actual phenomena from this theory to
disturbing causes. At the same time we confess that what we call
disturbing causes are simply those parts of the true circumstances
which we do not know or have neglected, and we endeavour in future to
take account of them. We thus acknowledge that the so-called
disturbance is a mere figment of the mind, not a fact of nature, and
that in natural action there is no disturbance.
But this is not the only way in which the harmony of the material with
the mental operation may be disturbed. The mind of the mathematician
is subject to many disturbing causes, such as fatigue, loss of memory,
and hasty conclusions; and it is found that, from these and other
causes, mathematicians make mistakes.
I am not prepared to deny that, to some mind of a higher order than
ours, each of these errors might be traced to the regular operation of
the laws of actual thinking; in fact we ourselves often do detect, not
only errors of calculation, but the causes of these errors. This,
however, by no means alters our conviction that they are errors, and
that one process of thought is right and another process wrong. I
One of the most profound mathematicians and thinkers of our time, the
late George Boole, when reflecting on the precise and almost
mathematical character of the laws of right thinking as compared with
the exceedingly perplexing though perhaps equally determinate laws of
actual and fallible thinking, was led to another of those points of
view from which Science seems to look out into a region beyond her own
domain.
"We must admit," he says, "that there exist laws" (of thought) "which
even the rigour of their mathematical forms does not preserve from
violation. We must ascribe to them an authority, the essence of which
does not consist in power, a supremacy which the analogy of the
inviolable order of the natural world in no way assists us to
comprehend."
***
Introductory Lecture on Experimental Physics.
James Clerk Maxwell
The University of Cambridge, in accordance with that law of its
evolution, by which, while maintaining the strictest continuity
between the successive phases of its history, it adapts itself with
more or less promptness to the requirements of the times, has lately
instituted a course of Experimental Physics. This course of study,
while it requires us to maintain in action all those powers of
attention and analysis which have been so long cultivated in the
University, calls on us to exercise our senses in observation, and our
hands in manipulation. The familiar apparatus of pen, ink, and paper
will no longer be sufficient for us, and we shall require more room
than that afforded by a seat at a desk, and a wider area than that of
the black board. We owe it to the munificence of our Chancellor,
that, whatever be the character in other respects of the experiments
which we hope hereafter to conduct, the material facilities for their
full development will be upon a scale which has not hitherto been
surpassed.
The main feature, therefore, of Experimental Physics at Cambridge is
the Devonshire Physical Laboratory, and I think it desirable that on
the present occasion, before we enter on the details of any special
study, we should consider by what means we, the University of
Cambridge, may, as a living body, appropriate and vitalise this new
organ, the outward shell of which we expect soon to rise before us.
The course of study at this University has always included Natural
Philosophy, as well as Pure Mathematics. To diffuse a sound knowledge
of Physics, and to imbue the minds of our students with correct
dynamical principles, have been long regarded as among our highest
functions, and very few of us can now place ourselves in the mental
condition in which even such philosophers as the great Descartes were
involved in the days before Newton had announced the true laws of the
motion of bodies. Indeed the cultivation and diffusion of sound
dynamical ideas has already effected a great change in the language
and thoughts even of those who make no pretensions to science, and we
are daily receiving fresh proofs that the popularisation of scientific
doctrines is producing as great an alteration in the mental state of
society as the material applications of science are effecting in its
outward life. Such indeed is the respect paid to science, that the
most absurd opinions may become current, provided they are expressed
in language, the sound of which recals some well-known scientific
phrase. If society is thus prepared to receive all kinds of
scientific doctrines, it is our part to provide for the diffusion and
cultivation, not only of true scientific principles, but of a spirit
of sound criticism, founded on an examination of the evidences on
which statements apparently scientific depend.