( 782 ) 
de 
. Now we 
da 
bi 
de En 
really — ae but which is now also represented by 
a 
notice that the energy of the repulsive forces is taken into account 
in the calculation of wp by simply excluding that part of the exten- 
sion where the molecules would have penetrated into the wall of 
the vessel or into each other. We may also say «, and ¢, are put 
= 0 when the molecules do not yet touch the walls, and if they 
do, put as oo. 
So the «, and «, have a discontinuous course, and yet it is just 
; fr: (ie ae 
on the assumption that a certain extension exists with finite —, 
a 
with respect to which it is integrated after multiplication by the 
density e 7 , that the method is based. So it is certainly desirable 
to question the validity of this method of calculation. Disregarding 
the repulsive and attractive forces between the molecules inter se, 
we have to Ge: 
p 
de T de, 
ne J 2) Pf Bat 
when we have integrated with respect to the velocities. So also: 
7 oT 
LW 7 O 7 Op 
amor! fe da tee: 
a 
Is it now allowed to take for this integral fi dz,... dz, integrated 
with respect to the extension limited by the walls of the vessel? 
Let us consider the simplest conceivable case of an ensemble of one 
2 
molecule with coordinate of height x. In fig. 1 e 7 is given as 
f(z). AC indicates the distance at which the molecule still repulses 
the wall. When now the piston is moved over a distance Aa, the 
line AB moves to A’ B’ (with or without change of form). The limit 
‚area AB B'A' 
of 7 now represents — fe Tde. In fig. 2 the distance 
ZA 
€) 
dl 
AC is reduced to 0, so that ¢, = if c>a,ande,=Oande T=1 
if «<a. The figure ABB'A' now becomes a rectangle, which therefore 
also represents A extension with basis Aa. When the area of these 
two figures becomes equal with decreasing Aa, we may take 
d 
dE OER 7 (then both =1). This is the case when in fig. 1 
da da 
