TRANSACTIONS OF SECTION A. 407 
This leaves still, unverified only one (M,;,) of Mersenne’s supposed primes, and 
14 out of his 44 supposed composites, viz., those given by 
q=101, 103, 107, 109, 137, 139, 149, 157, 167, 193, 199, 227, 229, 241. 
A complete list of all the possible prime divisors < one million of the 14 still 
unverified supposed composites has been prepared by M. A. Gérardin (of Nancy, 
France) and the author jointly (but working independently). These ‘ trial 
divisors’ have been tested by the author up to that same limit without success; 
every trial divisor was tried twice. 
MONDAY, SEPTEMBER 9. 
Joint Discussion with Section B on the Atomic Heat of Solids. 
(i) The Atomic Heat of Solids at Low Temperatures. 
By F. A. Linpemann, Ph.D. 
If the ordinary principles of mechanics are admitted as governing the move- 
ments of atoms, equipartition of energy is bound to be attained, as has been 
shown by Maxwell, Boltzmann, Jeans, and others, Therefore the atomic heat 
of a solid at constant volume should be exactly 3R. 
Planck has shown that the energy U of an electric charge capable of 
oscillating with frequency v and in equilibrium with radiation of frequency » 
and energy u per cm’, is 
_ 3chu 
~ 16rv? 
Therefore Rayleigh’s formula 
2cRT 
Pa eNAe 
should be strictly accurate. This is obviously false, as F, becomes co for A=0. 
According to Poincaré one is bound to find a similar formula if one assumes 
that an atomic collision is capable of representation by differential equations. 
Assuming that an oscillator can only emit definite, discontinuous quantums 
of energy, Planck showed that their magnitude is proportional to the frequency, 
and developed the formula 
2c°h 1 16rhy* 1 
ie Rel. on of See * hy 
@ar—1 exr—1 
where A is a new universal constant 6,55.10-" erg. sec., and « is = This formula 
appears to agree with experimental results. 
* Tf'a solid is composed of atoms held at a certain mean distance from one 
another by forces, whose presence is revealed by the phenomena of elasticity, 
&c., these atoms will act as oscillators, whose frequency is determined by the 
force holding them in equilibrium and by their mass. If these atoms are 
electrically charged, as appears to be the case in salts which are strongly 
ionised in solution, they must contain the energy 
3c3 3hv 
= ieee Te 
as there would otherwise be a continual leak of energy from matter to ether, 
or vice versd. The same holds good if the atoms are not charged, as in the 
diamond, for one can imagine them connected to charged atoms by a perfect 
