408 TRANSACTIONS OF SECTION A. 
conductor of heat. Therefore, as Einstein pointed out, the atomic heat of 
N atoms ought to be 
=~) he 
dU _ Eid b= 
AD vg? (1 
This formula is only approximately correct, and fails altogether if one 
inserts the true frequencies. These may be calculated from the Reststrahlen, 
from the compressibility, density, and atomic weight, or from the melting- 
point, density, and atomic weight. The last two methods are not nearly as 
exact as the first. 
According to Nernst and Lindemann the atomic heat of the metals, of the 
diamond, NaCl, KCl, NaBr, and KBr, may be accurately represented by 
SEN) 
KT KT] Err | 
Co=").R ta EEN ats hy 2, 
(e=- 1) e=-1) | 
where y is in the case of the salts the exact frequency as found by Rubens by 
means of the Reststrahlen. The second term in* the brackets is difficult to 
explain. As it leads one to expect reflection an octave below the Reststrahlen, 
where the salts are transparent it has been suggested that it represents potential 
whilst the first term denotes kinetic energy. That this simple formula is only 
valid for substances which crystallise in the regular system, suggests that the 
slow vibrations may not be capable of causing Reststrahlen on account of the 
grouping of the positive and negative charges. 
A fact that emerges clearly is that the free electrons, if there are any, can 
orly have a very small specific heat, for the atomic heats of conductors and 
non-conductors may be represented by practically identical curves. 
Further it may be shown that Nernst’s theorem is a consequence of the fact 
that the atomic heats are infinitely small at the absolute zero. 
(ii) On an Hypothesis as to the Nature of Planck’s Quantum of Action. 
By G. E. Greson, Ph.D. 
One of the chief difficulties in Planck’s original theory of radiation is the assump- 
tion of a discontinuous absorption and emission of energy by the resonators. Such 
a discontinuity is inconsistent with Maxwell’s equations, on which the fundamental 
relation between the energy, U, of a resonator and the energy density, w, of the sur- 
rounding field, viz. :— 
eee (1) 
Sav? 
is based. 
In a former paper! the author suggested an hypothesis by means of which this 
difficulty might be overcome. Let us suppose that the discontinuity is confined 
solely to the collisions between the molecules with which the resonators are connected, 
so that during the time between collisions the resonators are subject to the ordinary 
laws of electrodynamics. Let us further suppose that the discontinuity due to the 
collisions is such that the energy of the resonator immediately after the collision is 
an integral multiple of a certain quantity ¢, whose magnitude will be specified later. 
It can be shown ” that, in all cases open to experimental investigation, the logar:th- 
mic decrement of an electron, bound to its position of equilibrium by quasi-elastic 
forces, is so small that its loss or gain of energy during the free time of a molecule 
can only be a very small fraction of «. 
Let us consider the forced vibrations of a resonator in the time between two 
collisions, 
1 Verh. der Deutsch, Phys. Ges., xvi., p. 104, 1912. 
2 Loe. cit. 
