ee) 
( 783 ) 
the gas phase, and vice versa, but independent of the second phase 
determine the number of particles which may detach themselves from 
the surrounding homogeneous phase, i.e. which are able entirely to 
overcome the power of attraction of the phase in which they are 
found, and so can reach a space where if no external forces are 
active the potential energy is maximum and the kinetic pressure 
may therefore be put zero. ' 
However, a few objections may be advanced to the method fol- 
lowed Le. particularly with respect to the way in which the loss 
of energy is calculated when a molecule leaves the homogeneous 
phase. I am indebted to Prof. van per Waars Jr. for the following 
proof, in which these difficulties are evaded. 
Let .V’ be the number of molecules of one gram molecule, ES 
5 
its potential energy, then the potential energy which one molecule 
loses when it is removed from the phase to a place where the 
Co 
potential is zero, is ep The influence of the collisions which One 
molecule meets with from another, can be reduced to a pressure on 
the distance sphere, as this is frequently done in the derivation of 
the equation of state by the virial method. This pressure, which we 
a MRT 
shall call P, is equal to p + Or ea 
If we want to determine the chance that a molecule escapes from 
the phase through the capillary layer, we shall have to take this 
pressure into account. For it is not constant through the capillary 
layer, but will gradually decrease if we traverse the capillary layer 
from the liquid in the direction towards the vapour. 
If we choose the Z-axis normal to the capillary layer and if we 
think « (the radius of the distance sphere) so small compared with 
the thickness’ of the capillary layer that over the distance 25 we 
may consider the pressure P as a linear function of z, the force 
with which a molecule is pressed outside by the pressure P will be 
_aP ST 
equal to — ae —. So the total work which is exerted by P on 
uz 
1) Prof. vaN DER WAALS Jr. points out to me that these conditions need not 
always be satisfied in the neighbourhood of a wall as was mentioned in my pre- 
vious paper, which is easily seen if we think of liquid phases in the neighbourhood 
of their critical temperature. So if we want in general to define the thermodynamic 
potential kinetically im a definite case only by means of properties of this phase 
ilself, and not of coexisting phases — and this seems desirable to me in many 
respects — we must replace the definition by means of a non-attracting wall by 
the purely mathematic one given in the text. 
51 
Proceedings Royal Acad. Amsterdam. Vol, XIII 
