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that a wave converges from the infinite space where it has every- 
where the same phasis, exactly into the same point. Yet we are 
not justified in assuming, that this second movement occurs in 
nature. On this Prof. PLANcK’s considerations are based. He thinks 
that he has found his perfectly irreversible process in radiation 
which falls on a resonator. He makes this process really irreversible 
by excluding a certain number of movements as not occurring. In 
reality Prof. Puanck’s ideas differ less from those of Prof. Bourz- 
MANN than he thinks. For the latter calls a great many movements 
possible, but very improbable, and assumes justly, that such improb- 
able movements may occur both in phenomena of molecular move- 
ment and in phenomena of radiation. 
Prof. BoLTZMANN’s considerations seem to be chiefly as foliows. 
As basis of his considerations he takes the reversibility of all 
processes, as well mechanical as electrical and magnetical ones. 
From this follows that a process, in which the entropy increases, 
might also take place in the opposite direction, so that the entropy 
decreased. Apparently this is in contradiction with the experiment 
which teaches us, that only those processes occur, in which the 
entropy increases. To explain this apparent contradiction, Prof. 
BOLTZMANN argues as follows: 
If we know exactly the initial conditions of a system with 
n degrees of freedom, i.e. the n generalised coordinates and their 
fluctions at a given moment, and if we know the laws of all the 
forces, acting on the system, we can calculate the state of the 
system at any moment. If however we know at a given moment 
only »— 1 of the coordinates and their fluctions, we can in general 
calculate nothing for a later moment. The want of knowledge of 
one of the 2 n necessary data, makes not only that one coordinate 
indetermined for the future, but ail the coordinates. If we consider a 
gas as a system with many degrees of freedom, the condition would 
be exactly determined only then, if at a given moment we know 
exnctly the coordinates and their fluctions for every molecule sepa- 
rately. As we however never know them, we can never say how 
the condition in the next moment will be. Perfectly general laws 
for movement of heat can therefore not be drawn up. 
By varying the coordinates of the separate molecules, we can 
however obtain a great number of systems, all of which fulfil the 
conditions, which are required to call the system in question a gas 
or a solid substance with a certain temperature and under a certain 
pressure and which differ only in the coordinates of the separate 
molecules. The number of these systems is infinite. Now Prof. 
