Encyclopaedia Britannica > Volume 3, Athens-BOI

A T
are not, the method of dialysis, as employed by Graham,
would enable us to separate the molecules of smaller mass
from those of greater, as they would stream through porous
substances with greater velocity. We should thus be able
to separate a gas, say hydrogen, into two portions, having
different densities and other physical properties, different
combining weights, and probably different chemical pro¬
perties of other kinds. As no chemist has yet obtained
specimens of hydrogen differing in this way from other
specimens, we conclude that all the molecules of hydrogen
are of sensibly the same mass, and not merely that their
mean mass is a statistical constant of great stability.
But as yet we have not considered the phenomena which
enable us to form an estimate of the actual mass and
dimensions of a molecule. It is to Clausius that we owe
the first definite conception of the free path of a molecule
and of the mean distance travelled by a molecule between
successive encounters. He showed that the number of
encounters of a molecule in a given time is proportional to
the velocity, to the number of molecules in unit of volume,
and to the square of the distance between the centres of
two molecules when they act on one another so as to have
an encounter. From this it appears that if we call this
distance of the centres the diameter of a molecule, and the
volume of a sphere having this diameter the volume of a
molecule, and the sum of the volumes of all the molecules
the molecular volume of the gas, then the diameter of a
molecule is a certain multiple of the quantity obtained by
diminishing the free path in the ratio of the molecular
volume of the gas to the whole volume of the gas. The
numerical value of this multiple differs slightly, according
to the hypothesis we assume about the law of distribution
of velocities. It also depends on the definition of an
encounter. When the molecules are regarded as elastic
spheres we know what is meant by an encounter, but if
they act on each other at a distance by attractive or repul¬
sive forces of finite magnitude, the distance of their
centres varies during an encounter, and is not a definite
quantity. Nevertheless, the above statement of Clausius
enables us, if we know the length of the mean path and
the molecular volume of a gas, to form a tolerably near
estimate of the diameter of the sphere of the intense action
of a molecule, and thence of the number of molecules in
unit of volume and the actual mass of each molecule. To
complete the investigation we have, therefore, to determine
the mean path and the molecular volume. The first
numerical estimate of the mean path of a gaseous molecule
was made by the present writer from data derived from the
internal friction of air. There are three phenomena which
depend on the length of the free path of the molecules of a
gas. It is evident that the greater the free path the more
rapidly will the molecules travel from one part of the
medium to another, because their direction will not be so
often altered by encounters with other molecules. If the
molecules in different parts of the medium are of different
kinds, their progress from one part of the medium to
another can be easily traced by analysing portions of the
medium taken from different places. The rate of diffu¬
sion thus found furnishes one method of estimating the
length of the free path of a molecule. This kind of
diffusion goes on not only between the molecules of
different gases, but among the molecules of the same gas,
only in the latter case the results of the diffusion cannot
be traced by analysis. But the diffusing molecules carry
with them in their free paths the momentum and the energy
which they happen at a given instant to have. The
diffusion of momentum tends to equalise the apparent
motion of different parts of the medium, and constitutes
the phenomenon called the internal friction or viscosity of
gases. The diffusion of energy tends to equalise the
0 M 41
temperature of different parts of the medium, and constitutes
the phenomenon of the conduction of heat in gases.
These three phenomena—the diffusion of matter, of
motion, and of heat in gases—have been experimentally
investigated,—the diffusion of matter by Graham and
Loschmidt, the diffusion of motion by Oscar Meyer and
Clerk Maxwell, and that of heat by Stefan.
These three kinds of experiments give results which in
the present imperfect state of the theory and the extreme
difficulty of the experiments, especially those on the con¬
duction of heat, may be regarded as tolerably consistent
with each other. At the pressure of our atmosphere, and
at the temperature of melting ice, the mean path of a
molecule of hydrogen is about the 10,000th of a milli¬
metre, or about the fifth part of a wave-length of green light.
The mean path of the molecules of other gases is shorter
than that of hydrogen.
The determination of the molecular volume of a gas is
subject as yet to considerable uncertainty. The most
obvious method is that of compressing the gas till it
assumes the liquid form. It seems probable, from the great
resistance of liquids to compression, that their molecules
are at about the same distance from each other as that at
which two molecules of the same substance in the gaseous
form act on each other during an encoixnter. If this is the
case, the molecular volume of a gas is somewhat less than
the volume of the liquid into which it would be condensed
by pressure, or, in other words, the density of the molecules
is somewhat greater than that of the liquid.
Now, we know the relative weights of different molecules,
with great accuracy, and, from a knowledge of the mean
path, we can calculate their relative diameters approxi¬
mately. From these we can deduce the relative densities
of different kinds of molecules. The relative densities so
calculated have been compared by Lorenz Meyer with the
observed densities of the liquids into which the gases may
be condensed, and he finds a remarkable correspondence
between them. There is considerable doubt, however, as
to the relation between the molecules of a liquid and those
of its vapour, so that till a larger number of comparisons
have been made, we must not place too much reliance on
the calculated densities of molecules. Another, and perhaps
a more refined, method is that adopted by M. Van der
Waals, who deduces the molecular volume from the devia¬
tions of the pressure from Boyle’s law as the gas is com¬
pressed.
The first numerical estimate of the diameter of a molecule
was that made by Loschmidt in 1865 from the mean path
and the molecular volume. Independently of him and of
each other, Mr Stoney, in 1868, and Sir W. Thomson, in
1870, published results of a similar kind—those of Thomson
being deduced not only in this way, but from considerations
derived from the thickness of soap bubbles, and from the
electric action between zinc and copper.
The diameter and the mass of a molecule, as estimated
by these methods, are, of course, very small, but by no
means infinitely so. About two millions of molecules of
hydrogen in a row would occupy a millimetre, and about
two hundred million million million of them would weigh
a milligramme. These numbers must be considered as
exceedingly rough guesses ; they must be corrected by more
extensive and accurate experiments as science advances;
but the main result, which appears to be well established,
is that the determination of the mass of a molecule is a
legitimate object of scientific research, and that this mass
is by no means immeasurably small.
Loschmidt illustrates these molecular measurements by
a comparison with the smallest magnitudes visible by means
of a microscope. Nobert, he tells us, can draw 4000 lines
in the breadth of a millimetre. The intervals between
III. — 6