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A History of Science, Volume 3 by Henry Smith Williams

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permanent structure. Only the frictionless medium
was lacking to fulfil all the conditions of Helmholtz's
indestructible vortices. And at once Lord Kelvin bethought
him of the frictionless medium which physicists
had now begun to accept--the all-pervading ether.
What if vortex rings were started in this ether, must
they not have the properties which the vortex rings
in air had exhibited--inertia, attraction, elasticity?
And are not these the properties of ordinary tangible
matter? Is it not probable, then, that what we call
matter consists merely of aggregations of infinitesimal
vortex rings in the ether?

Thus the vortex theory of atoms took form in Lord
Kelvin's mind, and its expression gave the world what
many philosophers of our time regard as the most
plausible conception of the constitution of matter
hitherto formulated. It is only a theory, to be sure;
its author would be the last person to claim finality for
it. "It is only a dream," Lord Kelvin said to me, in
referring to it not long ago. But it has a basis in
mathematical calculation and in analogical experiment
such as no other theory of matter can lay claim to, and
it has a unifying or monistic tendency that makes it,
for the philosophical mind, little less than fascinating.
True or false, it is the definitive theory of matter of the
twentieth century.

Quite aside from the question of the exact constitution
of the ultimate particles of matter, questions as to
the distribution of such particles, their mutual relations,
properties, and actions, came in for a full share
of attention during the nineteenth century, though the
foundations for the modern speculations were furnished
in a previous epoch. The most popular eighteenth-
century speculation as to the ultimate constitution of
matter was that of the learned Italian priest, Roger
Joseph Boscovich, published in 1758, in his Theoria
Philosophiae Naturalis. "In this theory," according
to an early commentator, "the whole mass of which
the bodies of the universe are composed is supposed to
consist of an exceedingly great yet finite number of
simple, indivisible, inextended atoms. These atoms
are endued by the Creator with REPULSIVE and ATTRACTIVE
forces, which vary according to the distance. At very
small distances the particles of matter repel each other;
and this repulsive force increases beyond all limits as
the distances are diminished, and will consequently
forever prevent actual contact. When the particles
of matter are removed to sensible distances, the repulsive is
exchanged for an attractive force, which decreases
in inverse ratio with the squares of the distances,
and extends beyond the spheres of the most remote

This conception of the atom as a mere centre of force
was hardly such as could satisfy any mind other than
the metaphysical. No one made a conspicuous attempt
to improve upon the idea, however, till just at
the close of the century, when Humphry Davy was led,
in the course of his studies of heat, to speculate as to
the changes that occur in the intimate substance of
matter under altered conditions of temperature. Davy,
as we have seen, regarded heat as a manifestation of
motion among the particles of matter. As all bodies
with which we come in contact have some temperature,
Davy inferred that the intimate particles of every substance
must be perpetually in a state of vibration.
Such vibrations, he believed, produced the "repulsive
force" which (in common with Boscovich) he admitted
as holding the particles of matter at a distance from
one another. To heat a substance means merely to
increase the rate of vibration of its particles; thus also,
plainly, increasing the repulsive forces and expanding
the bulk of the mass as a whole. If the degree of heat
applied be sufficient, the repulsive force may become
strong enough quite to overcome the attractive force,
and the particles will separate and tend to fly away
from one another, the solid then becoming a gas.

Not much attention was paid to these very suggestive
ideas of Davy, because they were founded on the
idea that heat is merely a motion, which the scientific
world then repudiated; but half a century later, when
the new theories of energy had made their way, there
came a revival of practically the same ideas of the particles
of matter (molecules they were now called)
which Davy had advocated. Then it was that Clausius
in Germany and Clerk-Maxwell in England took up
the investigation of what came to be known as the
kinetic theory of gases--the now familiar conception
that all the phenomena of gases are due to the helter-
skelter flight of the showers of widely separated molecules
of which they are composed. The specific idea
that the pressure or "spring" of gases is due to such
molecular impacts was due to Daniel Bournelli, who
advanced it early in the eighteenth century. The idea,
then little noticed, had been revived about a century
later by William Herapath, and again with some success
by J. J. Waterston, of Bombay, about 1846; but it
gained no distinct footing until taken in hand by
Clausius in 1857 and by Clerk-Maxwell in 1859.

The considerations that led Clerk-Maxwell to take
up the computations may be stated in his own words,
as formulated in a paper "On the Motions and Collisions
of Perfectly Elastic Spheres."

"So many of the properties of matter, especially
when in the gaseous form," he says, "can be deduced
from the hypothesis that their minute parts are in
rapid motion, the velocity increasing with the temperature,
that the precise nature of this motion becomes
a subject of rational curiosity. Daniel Bournelli,
Herapath, Joule, Kronig, Clausius, etc., have
shown that the relations between pressure, temperature,
and density in a perfect gas can be explained by
supposing the particles to move with uniform velocities
in straight lines, striking against the sides of the containing
vessel and thus producing pressure. It is not
necessary to suppose each particle to travel to any
great distance in the same straight line; for the effect
in producing pressure will be the same if the particles
strike against each other; so that the straight line
described may be very short. M. Clausius has determined
the mean length of path in terms of the average
of the particles, and the distance between the centres
of two particles when the collision takes place. We
have at present no means of ascertaining either of these
distances; but certain phenomena, such as the internal
friction of gases, the conduction of heat through a gas,
and the diffusion of one gas through another, seem to
indicate the possibility of determining accurately the
mean length of path which a particle describes between
two successive collisions. In order to lay the
foundation of such investigations on strict mechanical
principles, I shall demonstrate the laws of motion of
an indefinite number of small, hard, and perfectly
elastic spheres acting on one another only during impact.
If the properties of such a system of bodies are
found to correspond to those of gases, an important
physical analogy will be established, which may lead
to more accurate knowledge of the properties of matter.
If experiments on gases are inconsistent with the hypothesis
of these propositions, then our theory, though
consistent with itself, is proved to be incapable of
explaining the phenomena of gases. In either case it is
necessary to follow out these consequences of the hypothesis.

"Instead of saying that the particles are hard,
spherical, and elastic, we may, if we please, say the
particles are centres of force, of which the action is
insensible except at a certain very small distance,
when it suddenly appears as a repulsive force of very
great intensity. It is evident that either assumption
will lead to the same results. For the sake of avoiding
the repetition of a long phrase about these repulsive
bodies, I shall proceed upon the assumption of perfectly
elastic spherical bodies. If we suppose those
aggregate molecules which move together to have a
bounding surface which is not spherical, then the
rotatory motion of the system will close up a certain
proportion of the whole vis viva, as has been shown by
Clausius, and in this way we may account for the value
of the specific heat being greater than on the more
simple hypothesis."[1]

The elaborate investigations of Clerk-Maxwell served
not merely to substantiate the doctrine, but threw a
flood of light upon the entire subject of molecular dynamics.
Soon the physicists came to feel as certain of
the existence of these showers of flying molecules making
up a gas as if they could actually see and watch their
individual actions. Through study of the viscosity of
gases--that is to say, of the degree of frictional opposition
they show to an object moving through them or
to another current of gas--an idea was gained, with the
aid of mathematics, of the rate of speed at which the
particles of the gas are moving, and the number of collisions
which each particle must experience in a given
time, and of the length of the average free path traversed
by the molecule between collisions, These measurements were
confirmed by study of the rate of diffusion
at which different gases mix together, and also by
the rate of diffusion of heat through a gas, both these
phenomena being chiefly due to the helter-skelter flight
of the molecules.

It is sufficiently astonishing to be told that such
measurements as these have been made at all, but the
astonishment grows when one hears the results. It appears
from Clerk-Maxwell's calculations that the mean
free path, or distance traversed by the molecules between
collisions in ordinary air, is about one-half-millionth of
an inch; while the speed of the molecules is such that
each one experiences about eight billions of collisions
per second! It would be hard, perhaps, to cite an
illustration showing the refinements of modern physics
better than this; unless, indeed, one other result that
followed directly from these calculations be considered
such--the feat, namely, of measuring the size of the
molecules themselves. Clausius was the first to point
out how this might be done from a knowledge of the
length of free path; and the calculations were made by
Loschmidt in Germany and by Lord Kelvin in England,

The work is purely mathematical, of course, but the
results are regarded as unassailable; indeed, Lord Kelvin
speaks of them as being absolutely demonstrative
within certain limits of accuracy. This does not mean,
however, that they show the exact dimensions of the
molecule; it means an estimate of the limits of size
within which the actual size of the molecule may lie.
These limits, Lord Kelvin estimates, are about the one-
ten-millionth of a centimetre for the maximum, and the
one-one-hundred-millionth of a centimetre for the
minimum. Such figures convey no particular meaning
to our blunt senses, but Lord Kelvin has given a
tangible illustration that aids the imagination to at
least a vague comprehension of the unthinkable smallness
of the molecule. He estimates that if a ball, say
of water or glass, about "as large as a football, were to
be magnified up to the size of the earth, each constituent
molecule being magnified in the same proportion,
the magnified structure would be more coarse-grained
than a heap of shot, but probably less coarse-grained
than a heap of footballs."

Several other methods have been employed to estimate
the size of molecules. One of these is based upon
the phenomena of contact electricity; another upon the
wave-theory of light; and another upon capillary attraction,
as shown in the tense film of a soap-bubble!
No one of these methods gives results more definite
than that due to the kinetic theory of gases, just outlined;
but the important thing is that the results obtained
by these different methods (all of them due to
Lord Kelvin) agree with one another in fixing the
dimensions of the molecule at somewhere about the
limits already mentioned. We may feel very sure indeed,
therefore, that the molecules of matter are not the
unextended, formless points which Boscovich and his
followers of the eighteenth century thought them. But
all this, it must be borne in mind, refers to the molecule,
not to the ultimate particle of matter, about which we
shall have more to say in another connection. Curiously
enough, we shall find that the latest theories as
to the final term of the series are not so very far afield
from the dreamings of the eighteenth-century philosophers;
the electron of J. J. Thompson shows many
points of resemblance to the formless centre of Boscovich.

Whatever the exact form of the molecule, its outline
is subject to incessant variation; for nothing in molecular
science is regarded as more firmly established than
that the molecule, under all ordinary circumstances,
is in a state of intense but variable vibration. The
entire energy of a molecule of gas, for example, is not
measured by its momentum, but by this plus its energy
of vibration and rotation, due to the collisions already
referred to. Clausius has even estimated the
relative importance of these two quantities, showing
that the translational motion of a molecule of gas accounts
for only three-fifths of its kinetic energy. The
total energy of the molecule (which we call "heat")
includes also another factor--namely, potential energy,
or energy of position, due to the work that has been
done on expanding, in overcoming external pressure,
and internal attraction between the molecules themselves.
This potential energy (which will be recovered
when the gas contracts) is the "latent heat" of Black,
which so long puzzled the philosophers. It is latent in
the same sense that the energy of a ball thrown into
the air is latent at the moment when the ball poises at
its greatest height before beginning to fall.

It thus appears that a variety of motions, real and
potential, enter into the production of the condition
we term heat. It is, however, chiefly the translational
motion which is measurable as temperature; and this,
too, which most obviously determines the physical
state of the substance that the molecules collectively
compose--whether, that is to say, it shall appear to
our blunt perceptions as a gas, a liquid, or a solid. In
the gaseous state, as we have seen, the translational
motion of the molecules is relatively enormous, the
molecules being widely separated. It does not follow,
as we formerly supposed, that this is evidence of a repulsive
power acting between the molecules. The physicists
of to-day, headed by Lord Kelvin, decline to
recognize any such power. They hold that the molecules
of a gas fly in straight lines by virtue of their inertia,
quite independently of one another, except at
times of collision, from which they rebound by virtue of
their elasticity; or on an approach to collision, in which
latter case, coming within the range of mutual attraction,
two molecules may circle about each other, as a
comet circles about the sun, then rush apart again, as
the comet rushes from the sun.

It is obvious that the length of the mean free path of
the molecules of a gas may be increased indefinitely by
decreasing the number of the molecules themselves in a
circumscribed space. It has been shown by Professors
Tait and Dewar that a vacuum may be produced artificially
of such a degree of rarefaction that the mean
free path of the remaining molecules is measurable in
inches. The calculation is based on experiments made
with the radiometer of Professor Crookes, an instrument
which in itself is held to demonstrate the truth of
the kinetic theory of gases. Such an attenuated gas
as this is considered by Professor Crookes as constituting
a fourth state of matter, which he terms ultra-

If, on the other hand, a gas is subjected to pressure,
its molecules are crowded closer together, and the
length of their mean free path is thus lessened. Ultimately,
the pressure being sufficient, the molecules are
practically in continuous contact. Meantime the enormously
increased number of collisions has set the molecules
more and more actively vibrating, and the temperature
of the gas has increased, as, indeed, necessarily
results in accordance with the law of the conservation
of energy. No amount of pressure, therefore, can
suffice by itself to reduce the gas to a liquid state. It
is believed that even at the centre of the sun, where the
pressure is almost inconceivably great, all matter is to
be regarded as really gaseous, though the molecules
must be so packed together that the consistency is
probably more like that of a solid.

If, however, coincidently with the application of
pressure, opportunity be given for the excess of heat
to be dissipated to a colder surrounding medium, the
molecules, giving off their excess of energy, become
relatively quiescent, and at a certain stage the gas becomes
a liquid. The exact point at which this transformation
occurs, however, differs enormously for
different substances. In the case of water, for example,
it is a temperature more than four hundred degrees
above zero, centigrade; while for atmospheric air
it is one hundred and ninety-four degrees centigrade
below zero, or more than a hundred and fifty degrees
below the point at which mercury freezes.

Be it high or low, the temperature above which any
substance is always a gas, regardless of pressure, is
called the critical temperature, or absolute boiling-
point, of that substance. It does not follow, however,
that below this point the substance is necessarily a
liquid. This is a matter that will be determined by
external conditions of pressure. Even far below the
critical temperature the molecules have an enormous
degree of activity, and tend to fly asunder, maintaining
what appears to be a gaseous, but what technically is
called a vaporous, condition--the distinction being that
pressure alone suffices to reduce the vapor to the liquid
state. Thus water may change from the gaseous to
the liquid state at four hundred degrees above zero,
but under conditions of ordinary atmospheric pressure
it does not do so until the temperature is lowered three
hundred degrees further. Below four hundred degrees,
however, it is technically a vapor, not a gas; but
the sole difference, it will be understood, is in the degree
of molecular activity.

It thus appeared that the prevalence of water in a
vaporous and liquid rather than in a "permanently"
gaseous condition here on the globe is a mere incident
of telluric evolution. Equally incidental is the fact
that the air we breathe is "permanently" gaseous and
not liquid or solid, as it might be were the earth's surface
temperature to be lowered to a degree which, in
the larger view, may be regarded as trifling. Between
the atmospheric temperature in tropical and in arctic
regions there is often a variation of more than one hundred
degrees; were the temperature reduced another
hundred, the point would be reached at which oxygen
gas becomes a vapor, and under increased pressure
would be a liquid. Thirty-seven degrees more would
bring us to the critical temperature of nitrogen.

Nor is this a mere theoretical assumption; it is a
determination of experimental science, quite independent
of theory. The physicist in the laboratory has
produced artificial conditions of temperature enabling
him to change the state of the most persistent gases.
Some fifty years since, when the kinetic theory was in
its infancy, Faraday liquefied carbonic-acid gas, among
others, and the experiments thus inaugurated have
been extended by numerous more recent investigators,
notably by Cailletet in Switzerland, by Pictet in France,
and by Dr. Thomas. Andrews and Professor James Dewar
in England. In the course of these experiments
not only has air been liquefied, but hydrogen also, the
most subtle of gases; and it has been made more and
more apparent that gas and liquid are, as Andrews long
ago asserted, "only distant stages of a long series of
continuous physical changes." Of course, if the temperature
be lowered still further, the liquid becomes a
solid; and this change also has been effected in the case
of some of the most "permanent" gases, including air.

The degree of cold--that is, of absence of heat--
thus produced is enormous, relatively to anything of
which we have experience in nature here at the earth
now, yet the molecules of solidified air, for example, are
not absolutely quiescent. In other words, they still
have a temperature, though so very low. But it is
clearly conceivable that a stage might be reached at
which the molecules became absolutely quiescent, as
regards either translational or vibratory motion. Such
a heatless condition has been approached, but as yet
not quite attained, in laboratory experiments. It is
called the absolute zero of temperature, and is
estimated to be equivalent to two hundred and seventy-
three degrees Centigrade below the freezing-point of
water, or ordinary zero.

A temperature (or absence of temperature) closely
approximating this is believed to obtain in the ethereal
ocean of interplanetary and interstellar space, which
transmits, but is thought not to absorb, radiant energy.
We here on the earth's surface are protected
from exposure to this cold, which would deprive every
organic thing of life almost instantaneously, solely by
the thin blanket of atmosphere with which the globe is
coated. It would seem as if this atmosphere, exposed
to such a temperature at its surface, must there be
incessantly liquefied, and thus fall back like rain to be
dissolved into gas again while it still is many miles
above the earth's surface. This may be the reason why
its scurrying molecules have not long ago wandered
off into space and left the world without protection.

But whether or not such liquefaction of the air now
occurs in our outer atmosphere, there can be no question
as to what must occur in its entire depth were we
permanently shut off from the heating influence of the
sun, as the astronomers threaten that we may be in a
future age. Each molecule, not alone of the atmosphere,
but of the entire earth's substance, is kept
aquiver by the energy which it receives, or has received,
directly or indirectly, from the sun. Left to itself, each
molecule would wear out its energy and fritter it off
into the space about it, ultimately running completely
down, as surely as any human-made machine whose
power is not from time to time restored. If, then, it
shall come to pass in some future age that the sun's
rays fail us, the temperature of the globe must gradually
sink towards the absolute zero. That is to say,
the molecules of gas which now fly about at such
inconceivable speed must drop helpless to the earth;
liquids must in turn become solids; and solids themselves,
their molecular quivers utterly stilled, may perhaps
take on properties the nature of which we cannot

Yet even then, according to the current hypothesis,
the heatless molecule will still be a thing instinct with
life. Its vortex whirl will still go on, uninfluenced by
the dying-out of those subordinate quivers that produced
the transitory effect which we call temperature.
For those transitory thrills, though determining the
physical state of matter as measured by our crude
organs of sense, were no more than non-essential incidents;
but the vortex whirl is the essence of matter
itself. Some estimates as to the exact character of
this intramolecular motion, together with recent theories
as to the actual structure of the molecule, will
claim our attention in a later volume. We shall also
have occasion in another connection to make fuller
inquiry as to the phenomena of low temperature.




[1] (p. 10). An Account of Several Extraordinary Meteors or
Lights in the Sky, by Dr. Edmund Halley. Phil. Trans. of
Royal Society of London, vol. XXIX, pp. 159-162. Read
before the Royal Society in the autumn of 1714.
[2] (p. 13). Phil. Trans. of Royal Society of London for 1748,
vol. XLV., pp. 8, 9. From A Letter to the Right Honorable
George, Earl of Macclesfield, concerning an Apparent Motion
observed in some of the Fixed Stars, by James Bradley, D.D.,
Astronomer Royal and F.R.S.



[1] (p. 25). William Herschel, Phil. Trans. for 1783, vol.
[2] (p. 30). Kant's Cosmogony, ed. and trans. by W. Hartie,
D.D., Glasgow, 900, pp. 74-81.
[3] (p. 39). Exposition du systeme du monde (included in
oeuvres Completes), by M. le Marquis de Laplace, vol. VI., p.
[4] (p. 48). From The Scientific Papers of J. Clerk-Maxwell,
edited by W. D. Nevin, M.A. (2 vols.), vol. I., pp. 372-374.
This is a reprint of Clerk-Maxwell's prize paper of 1859.



[1] (p. 81). Baron de Cuvier, Theory of the Earth, New York,
1818, p. 98.
[2] (p. 88). Charles Lyell, Principles of Geology (4 vols.),
(p. 92). Ibid., vol. III., pp. 596-598.
[4] (p. 100). Hugh Falconer, in Paleontological Memoirs, vol.
II., p. 596.
[5] (p. 101). Ibid., p. 598.
[6] (p. 102). Ibid., p. 599.
[7] (p. 111). Fossil Horses in America (reprinted from American
Naturalist, vol. VIII., May, 1874), by O. C. Marsh, pp.
288, 289.



[1] (p. 123). James Hutton, from Transactions of the Royal
Society of Edinburgh, 1788, vol. I., p. 214. A paper on
the "Theory of the Earth," read before the Society in
[2] (p. 128). Ibid., p. 216.
[3] (p. 139). Consideration on Volcanoes, by G. Poulett Scrope,
Esq., pp. 228-234.
[4] (p. 153). L. Agassiz, Etudes sur les glaciers, Neufchatel,
1840, p. 240.



[1] (p. 182). Theory of Rain, by James Hutton, in Transactions
of the Royal Society of Edinburgh, 1788, vol. 1 , pp.
[2] (p. 191). Essay on Dew, by W. C. Wells, M.D., F.R.S.,
London, 1818, pp. 124 f.



[1] (p. 215). Essays Political, Economical, and Philosophical,
by Benjamin Thompson, Count of Rumford (2 vols.), Vol. II.,
pp. 470-493, London; T. Cadell, Jr., and W. Davies, 1797.
[2] (p. 220). Thomas Young, Phil. Trans., 1802, p. 35.
[3] (p. 223). Ibid., p. 36.



[1] (p. 235). Davy's paper before Royal Institution, 1810.
[2] (p. 238). Hans Christian Oersted, Experiments with the
Effects of the Electric Current on the Magnetic Needle, 1815.
[3] (p. 243). On the Induction of Electric Currents, by Michael
Faraday, F.R.S., Phil. Trans. of Royal Society of London for
1832, pp. 126-128.
[4] (p. 245). Explication of Arago's Magnetic Phenomena, by
Michael Faraday, F.R.S., Phil. Trans. Royal Society of London
for 1832, pp. 146-149.



[1] (p. 267). The Forces of Inorganic Nature, a paper by Dr.
Julius Robert Mayer, Liebig's Annalen, 1842.
[2] (p. 272). On the Calorific Effects of Magneto-Electricity and
the Mechanical Value of Heat, by J. P. Joule, in Report of the
British Association for the Advancement of Science, vol. XII.,
p. 33.



[1] (p. 297). James Clerk-Maxwell, Philosophical Magazine
for January and July, 1860.


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