CAPACITY FOR HEAT OF METALS AT LOW TEMPERATURES. 
353 
If the assumptions underlying the theoretical equations are valid, then we must 
conclude that other energy than that required for the three degrees of freedom ascribed 
to the atom is necessary to account for the atomic heat. 
Jeans* has shown that if the atoms in a crystal do not rotate, then they must be 
kept in their direction by couples under whose influence they could carry out 
vibrations. 
It is possible that at the higher temperatures the energy associated with these 
vibrations contributes to the specific heat, but hitherto no quantitative expression has 
been given which would enable this hypothesis to be verified. 
(5) Theories of Atomic Heat which are not Based on the Quantum Theory. 
Callendar has proposed a different theory! of radiation ; according to his view, 
equipartition of energy is not possible in full radiation, because the higher frequencies 
are being continually degraded by the Doppler effect in isothermal emission under 
equilibrium conditions. The formula^ obtained for the representation of the atomic 
heat is applicable, at present, only to those substances possessing a single frequency 
and further hypotheses are necessary before it can be applied to the metals. 
Prof. Callendar has very kindly permitted us to include the following brief 
summary of his views in our paper. 
Callendar’s Theory of Specific Heat. 
“ The total heat E + PV per gramme atom of an isotropic substance, all the atoms of 
which have the same frequency v, should be of the form E + PY = 3PT (l + 2) e~ z 
(where 2 = bv/ T) when the substance is in equilibrium with full radiation in which the 
partial pressure p per unit range of frequency is given by Rayleigh’s formula, 
p dv — Gv 2 Te~ z dv. 
In this case the latent heat of emission or absorption per unit range and volume 
(in order to agree with Wien’s displacement law and the Doppler effect in isothermal 
emission), must be of the form (‘ Phil. Mag.,’ May, 1914, p. 874), 
T (dp/dT)v = C/T (1+2) e~% 
which agrees better with experiments on radiation than Planck’s formula, and has 
the advantage of being consistent with the classical thermodynamics. 
* ‘ La Th4orie du Rayonnement et les Quanta,’ p. 63, 1912, 
t ‘Phil. Mag.,’ May, 1914. 
J ‘Phil. Mag.,’ October, 1913. 
YOL. CCXIV.—A, 2 Z 
