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Sept. 25, 1873] 
NATURE 
439 
others, but we may communicate to them some property by 
which we may obtain evidence of their diffusion. 
For instance, if a horizontal stratum of air is moving hori- 
zontally, molecules diffusing out of this stratum into those above 
and below will carry their horizontal motion with them, and so 
tend to communicate motion to the neighbouring strata, while 
molecules diffusing out of the neighbouring strata into the moving 
one will tend to bring it to rest. The action between the strata is 
somewhat like that of two rough surfaces, one of which slides over 
the other, rubbing on it. Friction is the name given to this action 
~ between solid bodies ; in the case of fluids it is called internal 
friction or viscosity. 
It is in fact only another kind ot diffusion—a lateral diffusion 
of momentum, and its amount can be calculated from data derived 
from observations of the first kind of diffusion, that of matter. 
The comparative values of the viscosity of different gases were 
determined by Graham in his researches on the transpiration of 
gases through long narrow tubes, and their absolute values have 
been deduced from experiments on the oscillation of discs by 
Oscar Meyer and myself. 
- Another way of tracing the diffusion of molecules through 
calm air is to heat the upper stratum of the air in‘a yessel, and 
so observe the rate at which this heat is communicated to the 
lower strata. This, in fact, is a third kind of diffusion—that of 
energy, and the rate at which it must take place was calculated 
from data derived from experiments on viscosity before any direct 
experiments on the conduction of heat had been made. Prof. 
Stefan, of Vienna, has recently, by a very delicate method, 
succeeded in determining the conductivity of air, and he finds 
it, as he tells us, in striking agreement with the vaiue predicted 
by the theory. 
All these three kinds of diffusion—the diffusion of matter, of 
momentum, and of energy—are carried on by the motion of the 
molecules. The greater the velocity of the molecules and the 
farther they travel before their paths are altered by collision with 
other molecules, the more rapid will be the diffusion. Now we 
know already the velocity of the molecules, and therefore by ex- 
periments on diffusion we can determine how far, on an average, 
a molecule travels without ‘striking another. Prof. Clausius, of 
Bonn, who first gave us precise ideas about the motion of agita- 
tion of molecules, calls this distance the mean path of a mole- 
cule. Ihave calculated, from Prof. Loschmidt’s diffusion ex- 
periments, the mean path of the molecules of four well-known 
gases. The average distance travelled bya molecule between 
one collision and another is given in the table. It is a very 
small distance, quite imperceptible to us even with our best 
microscopes. Roughly speaking, it is about the tenth part of 
the length of a wave of light, which you know is a very small 
quantity. Of course the time spent on so short a path by such 
swift molecules must be very small. I have calculated the 
number of collisions which each must undergo in a second. 
They are given in the table and are reckoned by thousands of 
millions. No wonder that the travelling power of the swiftest 
molecule is but small, when its course is completely changed 
thousands of millions of times in a second. 
The three kinds of diffusion also take place in liquids, but the 
relation between the rates at which they take place is not so simple 
as inthe case of gases. The dynamical theory of liquids is not so 
well understood as that of gases, but the principal difference be- 
tween a gas and a liquid seems to be that in a gas each molecule 
spends the greater part of its time in describing its free path, and 
is for a very small portion of its time engaged in encounters with 
other molecules, whereas in a liquid the molecule has hardly any 
free path, and is always in a state of close encounter with other 
molecules. 
Hence in a liquid the diffusion ot motion from one molecule to 
another takes place much more rapidly than the diffusion of the 
molecules themselves, for the same reason that itis more expedi- 
tious ina dense crowd to pass on a letter from hand to hand 
than to give it to a special messenger to work his way through 
the crowd. I have here a jar, the lower part of which contains 
a solution of copper sulphate, while the upper part contains pure 
water. It has been standing here since Friday, and you see 
how little progress the blue liquid has made in diffusing itself 
through the water above. The rate of diffusion of a solution of 
sugar has been carefully observed by Voit. Comparing his re- 
sults with those of Loschmidt on gases, we find that about as 
much diffusion takes place in a second in gases as requires a day 
in liquids. 
The rate of diffusion of momentum is also slower in liquids 
than in gases, but by no means in the same proportion. The 
same amount of motion takes about ten times as long to subside 
in water as in air, as you will see by what takes place when I stir 
these two jars, one containing water and the other air. There is 
still less difference between the rates at which a rise of tempera- 
ture is propagated through a liquid and through a gas. 
In solids the molecules are stillin motion, but their motions 
are confined within very narrow limits. Hence .the diffusion of 
matter does not take place in solid bodies, though that of motion 
and heat takes place very freely. Nevertheless, certain liquids 
can diffuse through colloid solids, such as jelly and gum, and by- 
drogen can make its way through iron and palladium. 
We have no time to do more than mention that most wonder- 
ful molecular motion which is called clectrolysis. Here is an 
electric current passing through acidulated water, and causing 
oxygen to appear at one electrode and hydrogen at the other. 
In the space between, the water is perfectly calm, and yet two 
opposite currents of oxygen and of hydrogen must be passing 
through it. The physical theory of this process has been studied 
by Clausius, who has given reasons for asserting that in ordinary 
water the molecules are not only moving, but every now and _ 
then striking each other with such violence that the oxygen and 
hydrogen of the molecules part company, and dance about 
through the crowd, seeking partners which have become 
dissociated in the same way. In ordinary water these ex- 
changes produce, on the whole, no observable effect, but 
no sooner does the electromotive force begin to act than it 
exerts its guiding influence on the unattached molecules, and 
bends the course of each toward its proper electrode, till the 
moment when, meeting with an unappropriated molecule of the 
opposite kind, it enters again into a more or less permanent 
union with it till it is again dissociated by another shock. Elec- 
par therefure, is a kind of diffusion assisted by electromotive 
‘orce, 
Another branch of molecular science is that which relates to 
the exchange of molecules between a liquid and a gas. It in- 
cludes the theory of evaporation and condensation, in which the 
gas in question is the vapour of the liquid, and a‘so the theory of 
the absorption of a gas by a liquid of a different substance. The 
researches of Dr. Andrews on the relations between the liquid 
and the gaseous state have shown us that though the statements 
in our own elementary text-books may be so neatly expressed 
that they appear almost self-evident, their true interpretation 
may involve some principle so profound that, till the right man 
has laid hold of it, no one ever suspects that anything is left to 
be discovered. 
These, then, are, some of the fields from which the data of 
molecular science are gathered. We may divide the ultimate 
results into three ranks, according to the completeness of our 
knowledge of them. 
Tothe first rank belong the relative masses of the mole- 
cules of different gases, and their velocities in metres per 
second. ‘These data are obtained from experiments on the pres- 
sure and density of gases, and are known to a high degree of 
precision. 
In the second rank we must place the relative size of the 
molecules of different gases, the length of their mean paths, and 
the number of collisions in a second. ‘These quantities are de- 
duced from experiments on the three kinds of diffusion, Their 
received values must be regarded as rough approximations till 
the methods of experimenting are greatly improved. 
There is another set of quantities which we must place i the 
third rank, because our knowledge of them is neither precise, as 
in the first rank, nor approximate, as in the second, but is only 
as yet of the nature of a probable conjecture. These are the 
absolute mass of a molecule, its absolute diameter, and the 
number of moleoules in a cubic centimetre. We know the rela- 
tive masses of different molecules with great accuracy, and we 
know their relative diameters approximately. From these we 
can deduce the relative densities of the molecules themselves, 
So far we are on firm ground. 
The great resistance of liquids to compression makes it pros 
bable that their molecules must be 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 
encounter. This conjecture has been put to the test by Lorenz 
Meyer, who has compared the densities of different liquids with 
the calculated relative densities of the molecules of their vapours, 
and has found a remarkable correspondence between them. 
Now Loschmidt has deduced from the dynamical theory the 
