the Sise of Molecules. 699 
as 14°39, from which it follows that the diameter of the mer- 
cury molecule cannot exceed 2°6x 10-5. On finding that 
the determinations of the viscosity of mercury are regarded 
as uncertain by Meyer (Kinetic Theory, pp. 197, 295), I 
thought it legitimate to omit mercury-vapour from the table. 
§ 10. The values given in the table are in good agreement 
with the upper limit set by the density in the solid and liquid 
states. The density of solid hydrogen at —256° C. is about 
850 times that of the gas, from which the upper limit 
for o is found to be 3°47x10-%. For oxygen the similar 
quantity is 3°0x 10-%. The density of solid nitrogen is 1114 
times that of the gas, leading to the limit c=3°5 x 10~‘, while 
from the density of solid argon (1:396) we can deduce the 
limit o—= 3°56 x 10-°. 
The maximum density of water occurs in the liquid state 
aie 7. and this leads to the limit c=3°05 x 10-8, a limit 
which is below the value 3°39 x 10—5 given in the table above. 
The same occurrence, then, as was experienced with mercury- 
vapour finds place again in the case of water-vapour. It may 
be that the error affects all vapours, and that it is not legiti- 
mate, even as an approximation, to treat a vapour as a perfect 
gas (cf. Meyer, Kinetic Theory of Gases, p. 221 e¢ seq.). 
On the other hand, it is certainly illegitimate to treat 
molecules as elastic spheres, and the fact that we have assumed 
all molecules to be spheres must have introduced a large 
possibility of error. So long as we are dealing only with 
free path and collision formule, the error will affect all 
quantities about equally—we can, in fact, define o as the 
diameter of a sphere such that spheres of this diameter would 
undergo the same number of collisions as take place in the 
actual gas. But in considering the solid state, we are no 
longer dealing with free paths and collisions, so that if we 
continue to regard molecules as spheres a new definition of 
becomes necessary. In fact, we define o now as the diameter 
of a sphere which occupies the same space as the molecule, 
and the more the molecules differ from the spherical shape, 
the more this value of o will differ from the former value. 
We cannot therefore be surprised at some difference between 
the values obtained by the consideration of the solid state, 
and those obtained by the other methods we have used. 
The paper following may be regarded as an appendix to 
the present paper, explaining the calculation of the formule 
which have been used in the present paper. 
