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BoLTzZMANN has proved that for the vast majority of those systems, 
the state after a given time is of course not perfectly determined, 
but yet fulfils certain conditions, that namely the mean density and 
the mean kinetic energy in every volume element will be such 
that we may speak again of a solid or a gas of a certain tempera- 
ture and under a certain pressure. Of course this is not proved for 
the great majority of all systems occurring in nature, but for all 
imaginable systems which answer to our idea “substance of a certain 
temperature and under a certain pressure’. If we suppose all these 
different systems to be equally probable, we may say that it is 
highly improbable that we meet with a phenomenon, in which the 
entropy increases with a measurable amount. The supposition of 
Prof. BOLTZMANN thet these systems are equally probable, is not 
new. Every one who has written on kinetic gas theory could not 
but make this supposition though in a somewhat different formula- 
tion, in order to calculate the mean number of collisions and such 
like quantities. The fact that observations show that the entropy 
always increases, justifies the assumption that this supposition agrees 
with reality. Convinced of the correctness of these considerations of 
Prof. BOLTZMANN, I wanted to treat the entropy of radiation in a 
similar way. The H theorem of Prof. BOLTZMANN is closely connected 
with the distribution of velocities according to MAXWELL. Therefore I 
thought that I had in the first place to find the analogue of it for 
the distribution of the electric forces in a space, in which a great 
number of radiating molecules are to be found. This distribution 
will be treated in the following chapter. 
First some observations on an, in my opinion, essentiel conse- 
quence of the considerations of Prof. BOLTZMANN, viz that the entropy 
increases only in consequence of collisions. 
To show this we take the following process into conside- 
ration: 
The walls inclosing a quantity of gas are suddenly removed at 
the moment ¢, so that the gas spreads in an infinite vacuum. We 
leave the molecular attraction out of account. If we take the gas at 
a high degree of rarefaction and if the volume in which it was 
enclosed is supposed to be not too large, many molecules will move 
away without any collision. In order that we may apply Bontz- 
MANN’s H theorem, we must have a large quantity of molecules. 
The assumption that after the moment ¢ not a single molecule col- 
lides, may be in opposition to this requirement. Yet we may examine 
what might be the consequence of the assumption that all molecu- 
les moved away with the velocity which they had at the moment 
