( 585 ) 
viz., two uniform systems, of which the linear measures of the 
second are «-times larger, all masses g-times larger, and all charges 
of corresponding parts ~/a-times larger than of the first. it now 
appeared that when the velocities of the parts of the systems were 
the same, that then the ratio of the electrical forces in corresponding 
points was 13/a', so the ratio of the densities of energy 3/a*. Then, 
however, the ratio of the temperatures is as that of the kinetic energy of 
corresponding particles, i. e. 3:1, so that the law of BourzMANN is 
fulfilled only when 9‘ = #/a° or B= 1/a. As, however, it is always 
possible to imagine these systems in such a way that « is not 1/2, 
it appears that the thermodynamic laws of radiation are not fulfilled 
for arbitrarily chosen systems. So when we make arbitrary suppositions 
concerning the nature of the walls, we run a great risk of choosing 
them in such a way that the spectral distribution with which they 
would be in equilibrium, does not agree with the real normal 
spectrum, this could only be incidentally the case. And so there is 
no ground to assume that the two formulae of PLANCK mentioned 
represent the same spectrum, which removes the ground for the 
assumption of the energy-quanta. 
JEANS’) considers it a difficulty to assume that walls could be 
imagined for which the thermodynamic laws of radiation are not 
fulfilled. I do not see the difficulty. The thermodynamic laws are 
only empiric laws. And when we come to the conclusion that the 
radiation of arbitrarily imagined walls does not satisfy the second 
law of thermodynamics, whereas experience teaches that the real 
radiation does satisfy it, we have simply to conclude from this that 
such walls do not occur in nature. We should, indeed, meet with 
a difficulty, if we could show that the laws of thermodynamics had 
to be applicable to all conceivable systems. The statistical derivation 
of these laws seems really to imply this. This, however, is only 
seemingly the case. For any fictitious system, whatever properties 
we ascribe to it, a state of statistical equilibrium will, no doubt, 
exist which is characterized by the fact that a certain quantity, 
which we may call the probability, is maximum. If we call the 
logarithm of the probability entropy, then for every system the 
theorem will hold that with given energy and volume this entropy 
is maximum. But it has not been proved a priori that the entropy defined 
. 
rt: dQ ’ 
in this way, is always represented by es OE at least it has only 
been proved for mechanical systems, and not for electrical ones, 
1) J. H. Jeans, Phil. Mag. Series VI Vol. XII p. 57, 1906. 
