438 7 NATURE 
» 
[Sept 25, 1873 
published in 1847, made a much more extensive ‘application of 
the theory to gases, and Dr. Joule, whose absence from our 
meeting we must all regret, calculated the actual velocity of the 
molecules of hydrogen. 
The further development of the theory is generally sup- 
posed to have been begun with a paper by Kroénig, which does 
not, however, so far as I can see, contain any improvement on what 
had gone before. It seems, however, to have drawn the attention 
of Prof. Clausius to the subject, and to him we owe a very large 
part of what has been since accomplished. ‘ 
We all know that air or any other gas placed in a vessel 
presses against the sides of the vessel, and against the surface of 
any body placed within it. On the kinetic theory this pressure 
is entirely due to the molecules striking against these surfaces, 
and thereby communicating to them a series of impulses which 
follow each other in such rapid succession that they produce 
an effect which cannot be distinguished from that of a continuous 
pressure, 
If the velocity of the molecules is given, and the number 
varied, then since each molecule, on an average, strikes the side 
of the vessel the same number of times, and with an impulse of 
the same magnitude, each will contribute an equal share to the 
whole pressure. The pressure in a vessel of given size is 
therefore proportional to the number of molecules in it, that is to 
the quantity of gas in it. 
This is the complete dynamical explanation of the fact dis- 
covered by Robert Boyle, that the pressure of air is proportional 
to its density. It shows also that of different portions of gas 
forced into a vessel, each produces its own part of the pressure 
independently of the rest, and this whether these portions be of 
the same gas or not. 
Let us next suppose that the velocity of the molecules is in- 
creased. Each molecule will now strike the sides of the vessel a 
greater number of times in a second, but besides this, the impulse 
of each blow will be increased in the same proportion, so that 
the part of the pressure due to each molecule will vary as the 
Square of the velocity. Now the increase of the square of velocity 
corresponds, in our theory, to a rise of temperature, and in this 
Way we can explain the effect of warming the gas, and also the 
law discovered by Charles that the Proportional expansion of 
‘all gases between given temperatures is the same. 
The dynamical theory also tells us what will happen if 
molecules of different masses are allowed to knock about 
together. The greater masses will go slower than the smaller 
ones, so that, on an average, every molecule, great or small, 
will have the same energy of motion. 
The proof of this dynamical theorem,.in which I claim the 
priority, has recently been greatly developed and improved by 
Dr. Ludwig Boltzmann. “The most important consequence 
which flows from it is that a cubic centimetre of every gas at 
standard temperature and pressure contains the same number of 
molecules. This is the dynamical explanation of Gay Lussac’s 
law of the equivalent volumes of gases. But we must now 
descend to particulars, and calculate the actual velocity of a 
molecule of hydrogen. 
A cubic centimetre of hydrogen, at the temperature of 
melting ice and at a pressure of one atmosphere, weighs 
000008954 grammes. We have to find at what rate this small 
mass must move (whether altogether or in separate molecules 
makes no difference) so as to produce the observed pressure 
on the sides of the cubic centimetre, This is the calculation 
which was first made by Dr. Joule, and the result is 1,859 
metres per second. This is what we are accustomed to call a 
great velocity. It is greater than any velocity obtained, in 
artiliery practice. The velocity of other gases is less, as you 
will see by the table, but in all cases it is very great as compared 
with that of bullets, 
We have now to conceive the molecules of the air in this 
hall flying about in all directions, ata rate of about seventeen 
miles in a minute, 
If all these molecules were flying in the same direction, they 
would constitute a wind blowing at the rate of seventeen miles 
a minute, and the only wind which approaches this velocity is 
that which proceeds from the mouth of acannon. How, then, 
are you and I able to stand here? Only because the molecules 
happen to be flying in different directions, so that those which 
strike against our backs enable us to support the storm which is 
beating against our faces. Indeed, if this molecular bombard- 
ment were to cease, even for an instant, our veins would swell, 
our breath would leave us, and we should, literally, expire. But 
it isnot only against us or against the swalls of the room that | 
the molecules are striking. Consider the immense number of 
them, and the fact that they are flying in every possible direction, 
and you will see that they cannot avoid striking each other, 
Every time that two molecules come into collision, the paths of 
both are changed, and they go off in new directions. Thus 
each molecule is continually getting its course altered, so 
that in spite of its great velocity it may be a long time be- 
fore it reaches any great distance from the point at which it set 
out. 
I have here a bottle containing amnionia. Ammonia is a 
gas which you can recognise by its smell. Its molecules have a 
velocity of six hundred metres per second, so that if their course 
had not been interrupted by striking against the molecules of air 
in the hall, everyone in the most distant gallery would have 
smelt ammonia before I was able to pronounce the name of 
the gas. But instead of this, each molecule of ammonia is so 
jostled about by the molecules of air, that it is sometimes 
going one way and sometimes another. It is like a hare which 
is always doubling, and though it goes a great pace, it makes 
very little progress. Nevertheless, the smell of ammonia is now 
beginning to be perceptible at some distance from the bottle. 
The gas does diffuse itself through the air, though the process _ 
isa slow one, and if we could close up every opening of this | 
hall so as to make it air-tight, and leave everything to itself © 
for some weeks, the ammonia would become uniformly mixed 
through every part of the air in the hall. 
This property of gases, that they diffuse through each other, 
was first remarked by Priestley. Dalton showed that it takes 
place quite independently of any chemical action between the 
inter-diffusing gases, Graham, whose iFesearches were és- 
pecially directed towards those phenomena which seem to throw 
light on molecular motions, made a careful study of diftusion, 
and obtained the first results from which the rate of diffusion 
can be calculated. 
Still more recently the rates of diffusion of gases into each 
other have been measured with great precision by Prof. 
Loschmidt of Vienna. 
He placed the two gases in two similar vertical tubes, the 
lighter gas being placed above the heavier, so as to avoid the 
formation of currents, He then opened. a sliding valve, so as to 
make the two tubes into one, and after leaving the gases to them- 
selves for an hour or so, he shut the valve, and determined how 
much of each gas had diffused into the other. : 
As most gases are invisible, I shall exhibit gaseous diffusion to 
you by means of two gases, ammonia and hydrochloric acid, 
which, when they meet, form a solid product. The ammonia, 
being the lighter gas, is placed above the hydrochloric acid, with 
a stratum of air between, but you will soon see that the gases 
can diffuse through this stratum of air, and produce a cloud of 
white smoke when they meet. During the whole of this process 
no currents or any other visible motion can be detected, Every 
part of the vessel appears as calm as a jar of undisturbed air. 
But, according to our theory, the same kind of motion is going | 
on in calm air as in the inter-diffusing gases, the only difference _ 
being that we can trace the molecules from one place to another 
more easily when they are of a different nature from those 
through which they are diffusing, 
If we wish to form a mental representation of what is going on 
among the molecules in calm air, we cannot do better than ob- 
serve a swarm of bees, when every individual bee is flying 
furiously, first in one direction, and then in another, while the 
swarm, asa whole, either remains at rest, or sails slowly through 
the air, 
In certain seasons, swarms of bees are apt to fly off to a great 
distance, and the owners, in order to identify their a st 
when they find them on other people’s ground, sometimes throw 
handfulls of flour at the swarm. Now let us suppose that the 
flour thrown at the flying swarm has whitened those bees only 
which happened to be in the lower half of the swarm, leaving 
those in the upper half free from flour. 
If the bees still go on flying hither and thither in an irregular 
manner, the floury bees will be found in continually increasing 
proportions in the upper part of the swarm, till they have be- 
come equally diffused through every part of it. But the reason 
of this diffusion is not because the bees were marked with flour, 
but because they are flying about. The only effect of the marking 
is to enable us to identify certain bees, 
We have no means of marking a select number of molecules of 
air, so as to trace them after they have become diffused among 
