740 
x (3 ; 3 3 vS 1 
OS EN 2 log (2%Em) + log v — 7 log 5 NL ta log G} . (5) 
_ ~ = 
We must remark here that for a definite state of the gas the 
quantity in brackets is independent of the choice of the fundamental 
units of length, mass and time and that, therefore, the numerical value 
of S depends on this choice only in so far as this is the case with 4. 
This becomes evident when we remember that the dimensions of G 
are M3 L5 7-8. 
Pranck points out that in all probability G will be connected 
with the constant 4 which he has introduced into the theory of 
radiation and which, when multiplied by the frequency, determines 
the quantum of energy characteristic of a vibrator. As the dimen- 
sions of h are M/27'—! the elementary domain G must be propor- 
tional to /’. 
We have finally to make a special supposition about the magni- 
tude of the element G. If we combine » equal quantities of gas 
simply by putting them side by side, we certainly must assume 
that the entropy of the whole system will be equal to the sum of 
the ‘entropies of each of the quantities taken separately.. Thus S 
must be multiplied by ” when NV, v7 and Zare made » times greater. 
Now it follows from (5) that this is possible only when G also 
becomes 7 times greater, so that the elementary domain must be 
supposed to be proportional to the number of molecules of the quan- 
tity of gas considered. 
§ 4. It may be objected to Pranck’s considerations that he has 
failed to attach a physical meaning to his elementary domain G. 
As it would have six dimensions its magnitude would have to be 
determined by certain intervals for the coordinates and the momenta. 
Now, in so far as we are concerned with the coordinates we can 
hardly see why we should have to introduce intervals of a fixed 
finite value into our considerations of probability. To this objection 
PranckK replies that we must think of the relative coordinates of one 
molecule with respect to another and it must be owned indeed 
that a mutual action between the particles might give us a reason 
for introducing the finite intervals in question. In this line of thought 
PLanck ') even tries to account for the proportionality between G 
and the number of molecules. His reasoning may be reproduced as 
follows. Let all the molecules except one be already in their places 
and let Av,,Av,.... Avy—s be small elements of volume, each in 
1) Vorträge Wolfskehl-Kongress, p. 7 and 8. 
