the mass of the particles is variable, the fact that the normal pro- 
bability curve did hold good for the momenta would involve that 
it could not apply te the velocities. For Lorenrz-electrons the 
deviations from MAxweE.u’s law for the distribution of the velocities, 
occasioned by the variability of the mass, would remain small for 
temperatures which are practically reached. The average kinetic 
energy of electrons of that nature in the normal radiation field can 
probably be calculated as if the mass were constant. 
When we differentiate the value of the kinetic energy which we 
tind in this manner, according to the temperature we find c, as is 
well known, if only we add to it another term which accounts for 
the potential energy. 
§ 7. The potential energy. The distribution in space. 
For the distribution in space of particles of mass we have 
according to classical mechanics the following law: if » represents 
the number of particles per unit volume and « the potential energy 
of one particle, the expression 
ne’ =a constant throughout the space. . (12) 
For a mixture an expression of the same kind holds good for 
each of the components. If we wish to take into account the volume 
of the particles we may write that 
Ak haet be GAAND Ne ND 
V— 2b 
where |” represents the volume of the molecular weight in grams 
of the substance, and V—24 the “available space” present in this 
volume. The logarithm of this expression is, as’ is well known, 
equal to the thermodynamical potential *) of the component, to which 
the expression has relation. All thermodynamical equilibria, as well 
those for simple substances as those for mixtures, and also those in 
which electrically charged particles play a part, can be derived from 
the equation (124), which was for the first time used by BOLTZMANN. 
We will now consider the question how the space-distribution 
must be according to modified mechanics. Will this law of BOLTZMANN 
hold also according to them ? This question must be answered negatively. 
Let us imagine two coexisting phases e.g. liquid and vapour. 
Even if we assume that in each of the two phases Maxweti’s law 
for the distribution of the velocities is satisfied, the mean kinetic 
energy of the molecules in the two phases will be different. Of 
1) Or at least it differs from it only in a function of the temperature which is 
immaterial for the existence of thermodynamical equilibrium. 
