(580 ) 
Physics. — ‘On the law of the partition of energy in electrical 
systems.” By Prof. J. D. van peR Waats Jr., (Communicated 
by Prof. J. D. vaN DER WAALS). 
It is well known that MaxwrLr was the first to pronounce the 
thesis that in the case of statistical equilibrium every degree of 
freedom will possess on an average the same amount of kinetic 
energy. In my opinion BOLTZMANN's and GaBBs’s investigations have 
raised the validity of this thesis for the systems to which their 
theory applies, above doubt. And yet this result is difficult to recon- 
cile with the experimental data. It has already long been known 
that the gas molecules must undoubtedly possess more degrees of 
freedom than would follow from the specific heat at constant volume 
in connection with this law. 
BOLTZMANN *), GiBBs ®) and others have expressly stated that systems, 
as they occur in nature, always exhibit important points of difference 
with the systems for which the said law was proved. For BOLTZMANN 
and Gipss have drawn up their statistical theory exclusively for 
systems which have a finite number of degrees of freedom, and 
for which the equations of classical mechanics hold. The systems 
occurring in nature, on the other hand, always contain electrical 
charges; so we have always to deal with the ether with its infinite 
number of degrees of freedom. Moreover for the changes of the coordinates 
no longer the mechanical laws are exclusively to be taken into considera- 
tion, but also the fundamental equations of the theory of electricity. 
In view of this an extension of the statistical method, in such a 
way that it applied also to electrical phenomena, was urgently 
required. An attempt at such an extension was made by JHANs *) and 
by Lorentz *). They arrived both at the conclusion that also in this 
case the law of equal partition of energy holds. Their considerations, 
however, pointed out a new difficulty. When every degree of freedom 
possesses the same amount of kinetic energy, the ether with its 
infinite number of degrees of freedom would finally acquire all the 
energy. A consequence of this would be that in case of equilibrium 
between a material system and the ether, as is found in all heat 
phenomena in consequence of the radiation, the velocities of the 
molecules and the electrons would become zero. Moreover the ether 
would then have to contain the energy in such a way that all the 
1) L. Botrzmann, Wiener Sitzungsb. LXIIL p. 418. a. 1871. 
2) J W. Gress, Statistical Mechanics. p. 167. 
3) J. H. Jeans, Phil. Mag. Series VI. Vol. X, p. 91, 1905. 
4) H A. Lorentz, Nuovo Cimento, Series V. Vol. XVI. 
