1919-20.] 
Molecular Energy in Gases. 
may be presumed to be such that the atom is dynamically eqi 
a concentrated massive particle surrounded by a massless quasi-elastic 
envelope or fender. In an encounter the fenders take the blow and pre- 
vent the massive nuclei from close approach.* An encounter between two 
monatomic molecules whose masses are thus protected cannot be expected 
to communicate any rotational energy, if we make the very natural 
assumption that the fender does not transmit shearing stress. In that 
case the stress due to a blow is radial, and energy of translation only is 
taken up. 
Consider next a diatomic gas. The mass of the molecule is made up, we 
may suppose, of two concentrated particles held some way apart, and the 
“ fender ” of the molecule as a whole will have a surface of revolution about 
the line joining the two particles. Here again, if we assume the fender to 
be incapable of transmitting shearing stress, no energy of rotation about 
that line can be communicated by an encounter though the molecule is free 
to take up, and will take up, energy of rotation about any transverse axis. 
Thus one of its three degrees of rotational freedom is ineffective, the other 
two are effective, and the principle of equipartition gives the familiar 
result that, considered as a rigid body, its whole average energy, E'+E", 
is fRT, making C v = fR, C,p = |R, and y = T4. This is in accordance with 
the experimental fact that in general (subject to exceptions which will be 
referred to presently) a diatomic gas does exhibit very nearly these values 
of C v , C p , and y. The slightly greater value of y which is observed in 
normal air, etc. (1*402 or so), is readily accounted for by departure from 
the conditions postulated in the kinetic theory of an ideal gas, which 
make PV = RT. 
In this case also the Quantum Theory has been called in to explain a 
result which seems intelligible enough without it. The moment of inertia 
of a diatomic molecule about the line joining the two centres is of a much 
smaller order of magnitude than the moment about a transverse axis : it 
is of an order so small that the quantum of energy h 2 / 27 r 2 I with respect to 
rotation about that line is very large in comparison with the average energy 
of the blows which other molecules deliver, even when the gas is strongly 
heated. According to the Quantum Theory, therefore, energy of rotation 
about that line would not become established by encounters. About either 
transverse axis, however, the quantum of energy A 2 /2 7 r 2 I is far smaller, and 
* Cf. Perrin ( loc . cit.) : “Quant au rayon de protection, distance des centres au moment 
dn choc, il definit une distance pour laquelle la substance de l’atome exerce une force 
repulsive enorme sur la substance d’un autre atome. . . . En d’autres termes, chaque atome 
est condense au centre d’un mince armure spherique, relativement trks vaste, qui le protege 
contre l’approche des autres atomes.” 
