NATURE 
following remarkable proportion :—As the volume of a gas is to 
the combined volume of all the molecules contained in it, so is 
the mean path of a molecule to one-eighth of the diameter of 
a molecule. 
Assuming that the volume of the substance, when reduced to 
the liquid form, is not much greater than the combined volume 
of the molecules, we obtain from this proportion the diameter of 
amolecule. In this way Loschmidt, in 1865, made the first 
estimate of the diameter of a molecule. 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 
properties of metals. 
According to the table, which I have calculated from Lo- 
schmidt’s data, the size of the molecules of hydrogen is such that 
about two million of them in a row would occupy a millimetre, 
and a million million million million of them would weigh be- 
tween four and five grammes, 
In a cubic centimetre of any gas at standard pressure and tem- 
perature there are about nineteen million million million mole- 
cules. All these numbers of the third rank are, I need not tell 
you, to be regarded as at present conjectural. In order to 
warrant us in putting any confidence in numbers obtained in this 
way, we should have to compare together a greater number of 
independent data than we have as yet obtained, and to show that 
they lead to consistent results, 
Thus far we have been considering molecular science as an 
inquiry into natural phenomena. But though the professed aim 
of all scientific work is to unravel the secrets of nature, it has 
another effect, not less valuable, on the mind of the worker. It 
leaves him in possession of methods which nothing but scientific 
work could have led him te invent, and it places him in a 
position from which many regions of nature, besides that which 
he has been stulying, appear under a new aspect. 
The study of molecules has developed a method of its own, 
and it has also opened up new views of nature. 
When Lucretius wishes us to form a mental representation of 
the motion of atoms, he tells us to look at a sunbeam shining 
through a darkened room (the same instrument of research by 
which Dr, Tyndall makes visible to us the dust we breathe, ) and to 
observe the motes which chase each other in all directions through 
it. This motion of the visible motes, he tells us, is but a result of 
thefarmorecomplicated motion of the invisible atoms which knock 
the motesabout. In his dream of nature, as Tennyson tells us, he 
“ saw the flaring atom-streams 
And torrents of her myriad universe, 
Ruining along the illimitable inane, 
Fly on to clash together again, and make 
Another and another frame of things 
For ever.” 
And it is‘no wonder that he should have attempted to burst 
the bonds of Fate by making his atoms deviate from their 
courses at quite uncertain times and places, thus attributing to 
them a kird of irrational free will, which on his materialistic 
theory is the only explanation of that power of voluntary action 
of which we ourselves are conscious. 
As long as we have to deal with only two molecules, and 
have all the data given us, we can calculate the result of their 
encounter, but when we have to deal with millions of molecules, 
each of which has millions of encounters in a second, the com- 
plexity of he problem seems to shut out all hope of a legitimate 
solution, 
The modern atomists have therefore adopted a method which 
is I believe new in the department of mathematical physics, 
though it has long been in use in the Section of Statistics. 
When the working members of Section F get hold of a Report of 
the Census, or any other document containing the numerical data 
of Economic and Social Science, they begin by distributing the 
whole population into groups, according to age, income-tax, 
education, religious belief, or criminal convictions. The number 
of individuals is far too great to allow of their tracing the his- 
tory of each separately, so that, in order to reduce their labour 
within human limits, they concentrate their attention on a 
smail number of artificial groups. The varying number of indi- 
viduals in each group, and not the varying state of each indi- 
vidual, is the primary datum from which they work. 
This, of course, is not the only method of studying human nature. 
We may observe the conduct of individual men and compare it 
with that conduct which their previous character and their 
present circumstances, according to the best existing theory, 
[ Sept. 25, 1873 
would lead us to expect. Those who practise this method en- 
deavour to improve their knowledge of the elements of human 
nature, in much the same way as an astronomer corrects the 
elements of a planet by comparing its actual position with that 
deduced from the received elements. The study of human nature 
by parents and schoolmasters, by historians and statesmen, is 
therefore to be distinguished from that carried on by registrars 
and tabalators, and by those statesmen who put their faith in 
figures. The one may be called the historical, and the other 
the statistical method. 
The equations of dynamics completely express the laws of the - 
historical method as applied to matter, but the application of 
these equations implies a perfect knowledge of all the data. But 
the smallest portion of matter which we can subject to experiment 
consis‘s of millions of molecules, not one of which ever becomes 
individually sensible to us. We cannot, therefore, ascertain the 
actual motion of any one of these molecules, so that we are 
obliged to abandon the strict historical method, and to adopt 
the statistical method of dealing with large groups of molecules. 
The data of the statistical method as applied to molecular science 
are the sums of large numbers of molecular quantities. In 
studying the relations between quantities of this kind, we meet 
with a new kind of regularity, the regularity of averages, which 
we can depend upon quite sufficiently for all practical purposes, 
but which can make no claim to that character of absolute 
precision which belongs to the laws of abstract dynamics. : 
Thus molecular science teaches us that our experiments can 
never give us anything more than statistical information, and 
that no law deduced from them can pretend to absolute pre- 
cision. But when we pass from the contemplation of our 
experiments to that of the molecules themselves, we leave the 
world of chance and change, and enter a region where every- 
thing is certain and immutable, : 
The molecules are conformed to a constant type with a pre- 
cision which is not to be found in the sensible properties of the 
bodies which they constitute. In the first place the mass ofeach 
individual molecule, and all its other properties, are absolutely 
unalterable. Inthe second place the properties of all molecules 
of the same kind are absolutely identical, 
Let us consider the properties of two kinds of molecules, those 
of oxygen and those of hydrogen. 
We can procure specimens of oxygen from very different 
sources—from the air, from water, from rocks of every geo- 
logical epoch. The history of these specimens has been very 
different, and if, during thousands of years, difference of circum- 
stances could produce difference of properties, these specimens of 
oxygen would show it. 
In like manner we may procure hydrogen from water, from 
coal, or, as Graham did, from meteoric iron. Take two litres of ~ 
any specimen of hydrogen, it will combine with exactly one litre 
of any specimen of oxygen, and will form exactly two litres of 
the vapour of water. y 3 
Now if, during the whole previous history of either specimen, 
whether imprisoned in the rocks, flowing in the sea, or careering 
through unknown regions with the meteorites, any modification 
of the molecules had taken place, these relations would no 
longer be preserved. 
But we have another and an entirely different method of com- 
paring the properties of molecules. The molecule, though in- 
destructible, is not a hard rigid body, but is capable of 
internal movements, and when these are excited it emits rays, 
the wave-length of which is a measure of the time of vibration 
of the molecule. x ee 
Ly means of the spectroscope the wave-lengths of different 
kinds of light may be compared to within one ten-thousandth 
part. In this way it has been ascertained, not only that mole- 
cules taken from every specimen of hydrogen in our laboratories 
have the same set of periods .of vibration, but that light, having 
the same set of periods of vibration, is emitted from the sun and 
from the fixed stars. 
We are thus assured that molecules of the same nature as 
those of our hydrogen exist in those distant regions, or at least 
did exist when the light by which we see them was emitted, 
From a comparison of the dimensions of the buildings of th 
Egyptians with those of the Greeks, it appears that they have a 
common measure. Hence, even if no ancient author had recorded 
the fact that the two nations employed the same cubit as a 
standard of length, we might prove it from the buildings them- 
selves. We should also be justified in asserting that at some 
time or other a material standard of length must have been 
