110 Proceedings of the Royal Society of Edinburgh. [Sess. 
in dealing with vibrations the energy- quantum involves a frequency which 
is determined by the nature of the vibrating body. 
The Planck formula is undoubtedly in good general agreement with 
what is known about the specific heat of gases, both as to the effect of 
vibrations of the infra-red type in contributing to the total energy, and as 
to the practically negligible effect of those of high frequency. The measured 
values of the specific heat in gases are scarcely definite enough to supply 
material for a quantitative comparison between them and the values that 
are deduced from the formula. But it may be questioned whether even a 
quantitative agreement would be decisive, for the general type of curve that 
is given by Planck’s formula is found in other physical phenomena — as 
for instance in the phenomena of magnetisation, where the constraint of 
the molecules resulting from their mutual forces accounts for similar char- 
acteristics in the curve. It would be easy, therefore, to base too much on 
the fact that the observed changes in molecular energy are adequately 
represented by means of such a curve. On the other hand, it may be 
pointed out that such a curve is found in the process of magnetisation 
only because that process results from the action of indivisible units or 
quanta, namely, the molecular magnets. This consideration suggests that 
the apparent antagonism between the older dynamics and the Quantum 
Theory may not impossibly disappear when the real nature of the electrical 
or magnetic atomicity which determines the quantum is understood. 
Summary. 
A review of known facts about the specific heat of gases, at tempera- 
tures ranging from low values up to 2000° C., points to the following 
conclusions : — 
1. The increase in specific heat which is observed to occur in most 
gases when they are heated is due to the setting up of to-and-fro vibrations 
of the atoms composing the molecules. The principle of equipartition 
does not apply to these vibrations. 
2. In monatomic gases substantially all the energy, so far as that is 
communicable, consists of energy of translation. Accordingly the specific 
heat is sensibly constant, C„ having the value fR and y the value If. 
3. In diatomic gases, under normal conditions, the energy consists 
mainly of energy of translation and energy of rotation about axes trans- 
verse to the line joining the two atoms. The specific heat C„ is approxi- 
mately fR, and two-fifths of this quantity is accounted for by there being 
two (and only two) effective degrees of freedom of rotation. The normal 
