( 540 ) 
This formula ean be used to determine s, if we know the manner 
in which n depends on z. We easily see from (XIII), that, just as 
VAN DER Waars supposed, the entropy in each element of volume 
depends only on the density n and on the number of collisions in 
that element'). We could expect this, having found exactly the same 
condition of equilibrium to which his theory leads. 
It must, however, not been forgotten that the whole above develop- 
ment and therefore the hypothesis of var per Waars are only valid, 
if the assumptions about the attractive forces introduced at p. 526 
and 527 are true. The changes that will have to be made in the 
theory, when these assumptions are relinquished, must be a matter 
of further examination *). 
7. Finally I shall determine the force exerted in a horizontal 
direction by the system. Consider a system identical with the former ; 
only let the section be no longer equal to unit of area, but let it be 
o. It is easily seen that this has no influence at all on the former 
developments. The density n, and the energy ¢, are determined by 
analogous equations; the only difference is that 7, (the number of 
molecules in the layer dz,,) is now given by n, 0dz,. instead of 
by n, dz,. 
For 4” we have therefore the formula 
k 
yr 4 Wz £, \ 
== — = Const. En py on, log == = == 
0) n, 0) 
l 
vA 
ty o 
= Const. + fn 1 —— 5) de WE ly eee 
n () 
0 
The average component, corresponding to the parameter 0, of the 
force exerted by the systems of the ensemble is given — as GrBBs 
showed — by the relation 
=: dy 
KT er ea oe er 
do 
The force A,, exerted by the systems of maximum frequency, is 
equal to the average force A,. Therefore equation (XIV) may be 
used to determine the force in a real system. Before I use (15) to 
1) The function w is connected with this number. 
2) In this examination the function S (mz, dz-) introduced in my dissertation will 
have to play a part. 
