107 
1919-20.] Molecular Energy in Gases. 
except in finite quantities equal to h/ir or an integral multiple of h/ir.* A 
solution may conceivably be found in the idea that the molecule is not 
really free to turn — that there is a constraint to be overcome, an action 
say, between it and the ether due to forces on the electrons. It may be 
admitted, from the known facts about the absorption and emission of 
radiant energy, that the ether must be regarded as forming part of the 
dynamical system. But one naturally seeks an escape from the application 
of the Quantum Theory to the rotation of the molecules, and the following 
suggestion is tentatively offered as an alternative. Eucken’s result would 
be explicable if we might suppose that under extreme cold the hydrogen 
molecule tends to assume a different form, by a coming together of the two 
atoms which are held apart at ordinary temperatures. Imagine the pair 
of massive particles to come together, without coalescing, but so close as 
to constitute what is virtually a single-atom molecule of double mass : 
the properties of a monatomic gas would then be simulated, and there would 
be no communicable rotation. The specific heats would then depend only on 
translation, and their theoretical values would agree with the observed values. 
If we accept this view it may be conjectured that the paired atoms come 
together when the rotational speed of the diatomic molecule falls below a 
certain limit, perhaps like the balls of an unstable centrifugal governor, and 
remain together until they are forced apart by a violent encounter. There 
are obvious difficulties in such a hypothesis, both as to the coming together 
of the atoms and their separation to restore the usual diatomic form to the 
molecule when the gas is reheated ; but they are perhaps less formidable 
than those that are involved in extending the idea of quanta to the angular 
momentum of a free body. 
A curious point may be noted in passing. If the hypothesis here 
suggested be valid, it appears likely that there may be hysteresis in the 
relation of the specific heat to the temperature when hydrogen is cooled to 
and warmed from a very low temperature. The dynamical conditions that 
would bring the pair of atoms in a molecule close together are different 
from those that would set them apart again ; the parting would probably 
require a higher temperature. One might expect, therefore, to find the 
change of structure exhibit hysteresis, resembling that which occurs in the 
passage of iron from one to another of two allotropic states. 
* Taking hv as the quantum of kinetic energy of rotation, the corresponding quantum 
of angular momentum is hi*. The theory requires that no blow should communicate 
angular momentum at all unless it communicates as much as this, whether we regard the 
indivisible quantum concerned in the operation as so much energy hv or as so much 
u action” h, the dimensions of which are those of angular momentum. 
