133, 134] Van der Waals' Equation 111 



Ndv 



or r , 



v b 



where b = f NTT^ (278), 



in which the distinction between N 1 and N is now ignored. The effect 

 of allowing for the finite size of the molecules in the calculation of the 

 pressure is therefore the same as that of reducing the volume from v to v b. 

 To allow for this, then, we replace equation (275) by 



p(v-b) = RNT (279). 



The value of 6, it is of interest to notice, is four times the aggregate sum 

 of the volumes of the molecules in the gas. 



The use of the calculus of probabilities which is made in this argument 

 is probably open to criticism. We shall not stop to discuss the validity or 

 non-validity of the argument, as we shall subsequently arrive at exactly the 

 same result by a method which does not rely on the calculus of probabilities 

 for its justification. 



134. The principle underlying Van der Waals' correction for cohesion is 

 as follows. It is supposed that when the " spheres of molecular action " of 

 two molecules do not intersect, the forces between the molecules, although 

 small, are not negligible. Accordingly we suppose that a molecule in the gas 

 is subjected to forces of cohesion acting between it and all the neighbouring 

 molecules. The resultant of these forces varies continually both in direction 

 and magnitude, with the position of the molecules. When the molecule is 

 sufficiently far removed from the surface, all directions are equally likely for 

 this resultant, and hence the aggregate force, averaged over a sufficient 

 length of time, will be nil. When, however, the molecule is at or near the 

 surface this is no longer true. Let the force from each molecule be resolved 

 into tangential arid normal components. Then all directions in the tangent 

 plane are equally likely for the tangential components, but the normal com- 

 ponent is in the majority of cases directed inwards. Averaged over a 

 sufficient length of time the resultant force will therefore be a normal force 

 always directed inwards. 



We have here supposed the radii of curvature of the surface to be so 

 large compared with molecular dimensions that the surface may at every 

 point be regarded as plane. In this case the conditions will be the same at 

 every point of the surface, and the normal force will depend only on the 

 density of the gas, and the distance from the boundary of the point at which 

 this force is estimated. 



Thus the average effect of the forces of cohesion can be represented by a 

 permanent field of force acting at and near the surface. It is this field of 

 force which jnay be regarded as giving rise to the phenomena of capillarity 

 and surface-tension in liquids. Now if we follow Van der Waals in supposing 



