104 Proceedings of the Royal Society of Edinburgh. [Sess. 
its molecules, C„ being practically equal to fR, to fR, and y to If, when 
the condition as to density is such that the postulates of the kinetic theory 
approximately apply. In any gas for which these postulates hold, we may 
write 
E = E' + E" + E'", 
where E is the whole communicable energy, E' is the part of it which is 
due to translation of the molecules, E" the part due to rotation of the 
molecules, and E'" the part due to vibration within the molecules. C„ is of 
course c£E/c£T, and E' is f RT. 
The fact that in all monatomic gases y is found to be exactly or very 
nearly equal to If, and to retain that value even when the gas is strongly 
heated, shows that in such gases E" as well as E'" is negligible. In the 
course of its encounters the molecule acquires no rotation, or at least none 
that contributes appreciably to the energjr. Although, according to prevail- 
ing modern conceptions of atomic structure, the moment of inertia of a 
single-atom molecule about any axis through its centre is excessively small, 
owing to concentration of the mass in the positive nucleus, it must be 
regarded as finite, and the principle of equipartition might seem to demand 
that each of the three degrees of freedom of rotation should take up an 
amount of energy equal to f RT. The aid of the Quantum Theory has been 
invoked to explain why this does not occur.* According to that explanation 
the least amount of energy of rotation which a molecule can acquire during 
an encounter is hv, where v is the number of turns per second and h is 
Planck’s constant ; hence the least possible speed of rotation v 0 is given by 
the equation 
hv 0 = 
from which 
h 
V ° 2tt 2 I ’ 
and the quantum of energy of rotation is 
W 
27T 2 I' 
In a monatomic molecule the moment of inertia I is excessively small and 
the quantum is consequently so large as greatly to exceed the whole energy 
of the striking molecule, with the result that no energy of rotation passes 
during the encounter. This extension of the theory of quanta to the 
rotational kinetic energy of a body that is free to revolve in space without 
constraints seems to me unnecessary. For the forces in and about an atom 
* E.g. in Perrin’s Les Atomes, art. 94. 
