72 The Law of Distribution [CH. v 



vanishes so long as no two molecules or no molecule and the boundary 

 overlap, and becomes infinite if this takes place. Or, what is the same 

 thing, <I> vanishes throughout all those parts of the generalised space which 

 were retained in 33, and becomes infinite throughout those parts which 

 were excluded. The parts which were excluded might have been supposed 

 to be determined either by the condition that <I> should be greater than zero, 

 or that <E> should be infinite. 



In the present instance we shall suppose all regions excluded for which 



4>>e ................................. (170). 



If e is small in comparison with @, equation (169) may, without per- 

 ceptible error, be replaced by the equation 



as has been done throughout this Chapter. 



If e is so great that a system is only inside the region defined by the 

 inequality (170) throughout an infinitesimal fraction of its whole path, then 

 the results obtained in this Chapter (which in strictness apply only to a gas 

 in the non-excluded region) may be supposed to apply to a gas throughout 

 its whole path. 



In virtue of the assumption which it was announced that we were going 

 to make in 74, and for which experimental justification was given, it is 

 possible to choose e so that these two conditions shall be satisfied simul- 

 taneously. We therefore agree that the region in which <t> > e is to be 

 excluded from the generalised space, where e is chosen in this way. 



The effective molecular density can now be determined exactly as in 

 Chapter IV. We are, however, ignorant of the particular nature of the 

 intermolecular forces which occur in nature, and it would hardly be profitable 

 to try to determine the effective molecular density in general terms. It 

 will perhaps be sufficient to remark that it is a function not only of x, y, z 

 the coordinates of the point in space, but also of the type of molecule 

 which we are supposing to be found there, and also of the internal positional 

 coordinates of this molecule, if we assume the intermolecular forces to 

 depend on these coordinates. 



Sphere of Molecular Action. 



82. In this connection, the conception of a "sphere of molecular action " 

 is sometimes useful. We assume that a sphere of diameter a- can be drawn 

 about the centre of gravity of every molecule, such that 



(i) the intermolecular forces between two molecules are inappreciable, 

 so long as the two " spheres of molecular action " do not intersect, 



