Aug. 14, 1873) 
of this subject is confessedly so difficult, that it is only 
recently that Prof. Stefan of Vienna,* by means of a very 
ingenious method, has obtained the first experimental 
determination of the conductivity of air, This result is, 
as he says, in striking agreement with the kinetic theory 
of gases. 
The experiments on the interdiffusion of gases, as 
conducted by Prof. Loschmidt and his pupils, appear 
to be far more independent of disturbing causes than any 
experiments on viscosity or conductivity. The inter- 
diffusing gases are left to themselves in a vertical cylin- 
drical vessel, the heavier gas being underneath. No 
disturbing effect due to currents seems to exist, and the 
results of different experiments with the same pair of 
gases appear to be very consistent with each other. 
They prove conclusively that the co-efficient of diffusion 
varies inversely as the pressure, a result in accordance 
with the kinetic theory, whatever hypothesis we adopt as 
to the nature of the mutual action of the molecules during 
their encounters, 
They also show that the co-efficient of diffusion in- 
creases as the temperature rises, but the range of 
temperature in the experiments appears to be too small 
to enable us to decide whether it varies as T?, as it should 
be according to the theory of a force inversely as the fifth 
power of the distance adopted in my paper in the 
Phil. Trans, 1866, or as T! as it should do according to 
the theory of elastic spherical molecules, which was the 
hypothesis originally developed by Clausius, by myself in 
the Phil. Mag. 1860, and by O. E. Meyer. 
In comparing the co-efficients of diffusion of different. 
pairs of gases, Prof. Loschmidt has made use of a 
formula according to which the co-efficient of diffusion 
should vary inversely as the geometric mean of the 
atomic weights of the two gases. Iam unable to see 
any ground for this hypothesis in the kinetic theory, 
which in fact leads to a different result, involving the 
diameters of the molecules, as well as their masses. 
The numerical results obtained by Prof Loschmidt do 
not agree with his formula in a manner corresponding to 
the accuracy of his experiments. They agree in a very 
remarkable manner with the formula derived from the 
kinetic theory. 
I have recently been revising the theory of gases 
founded on that of the collisions of elastic spheres, using, 
however, the methods of my paper on the dynamical 
theory of gases (Phil. Trans, 1866) rather than those of 
my first paper in the Phil. Mag., 1860, which are more 
difficult of application, and which led me into great con- 
fusion, especially in treating of the diffusion of gases, 
The co-efficient of interdiffusion of two gases, accord- 
ing to this theory, is— 
120 / 7 
Parr asap ans) ox anes 
where w, and w, are the molecular weights of the two 
gases, that of hydrogen being unity. 
Sy is the distance between the centres of the mileeutes 
at collision in centimetres, 
V is the “velocity of mean square” of a molecule of 
hydrogen at o° C, 
V= a/ of = 185,900 centimetres per second. 
* Sitzh. d, k, Akad,, Feb, 22, 1874, 
NATURE PEt bags 
Wis the number of molecules in a cubic centimetre at 
0° C. and 76 cm. &, (the same for all gases), 
ee is the co-efficient of interdiffusion of the two gases 
(centimetre)? 
second measure. 
We may simplify this expression by writing— 
4 I I I 
a= —— _, o,,2 = — — a= 2 
aon iN). * gees Wy, | We @) 
Here a is a quantity the same for all gases, but involv- 
ing the unknown number N, 
o is a quantity which may be deduced from the corre- 
sponding Segment of M. Loschmidt. We have thus— 
Sig = 4049 (3) 
or the iaage between the centres of the molecules at 
collision is proportional to the quantity o, which may be 
deduced from experiment. 
If d, and d@, are the diameters of the two molecules, 
Sia = 3(G, + 4). 
Hence if@= a8... oy = $(5, + 4,). (4) 
Now M. Loschmidt has determined D for the six pairs 
of gases which can be formed from Hydrogen, Oxygen, 
Carbonic Oxide, and Carbonic Acid. The six values of ¢ 
deduced from these experiments ought not to be inde- 
pendent, since they may be deduced from the four values 
of § belonging to the two gases. Accordingly we find, by 
assuming 
TABLE I, 
d(H) = 1'739 
6(O) = 2'283 
6(CO) = 2°461 
8(CO,) = 2°75 
Observed 
Calculated wh I SSS 
Lae] = I I 
(3, + 5) *“D a, + Te 
For H and O 2'OIL I'992 
For H and CO 2"100 2116 
For H and CO, 2°257 2°260 
For O and CO 2°372 2°375 
For O and CO, 2°529 2°545 
For CO and CO, 2°618 2°599 
NOTE.—These numbers must be multiplied by 0°6 to 
reduce them to (centimetre-second) measure from the 
(metre-hour) measure employed by Loschmidt. 
The agreement of these numbers furnishes, I think, 
evidence of considerable strength in favour of this form 
of the kinetic theory, and if it should be confirmed by the 
comparison of results obtained from a greater number of 
pairs of gases it will be greatly strengthened. 
Evidence, however, of a higher order may be furnished 
by a comparison between the results of experiments of 
entirely different kinds, as for instance, the coefficients of 
diffusion and those of viscosity. If » denotes the co- 
efficient of viscosity, and p the density of a gas at o° C, 
and 760 mm, B, the theory gives— 
Bit iste 
Bead a/2 a (5) 
so that the following relation exists between the viscosi- 
ties of two gases and their coefficient of interdiffusion— 
= He f 
Dy = 5 mal Fs (6) 
‘ae 
