81-83] Intermolecular Forces 73 



(ii) when two " spheres of molecular action " intersect, the time which 

 elapses before they again separate is inappreciable in comparison 

 with the average time between two consecutive collisions of the 

 same molecule, a collision now being supposed to take place when- 

 ever two spheres intersect. 



It will be noticed that although the quantity a- is at our disposal, yet 

 we have to assume it to satisfy two distinct conditions, and these will not, 

 in general, be satisfied by the same values of <r. There is no experimental 

 justification for assuming that in the case of an actual gas they can be 

 satisfied simultaneously : the sole merit of the conception of a " sphere of 

 molecular action," is that it introduces a certain definiteness into a class 

 of problems of which the treatment otherwise is often impracticable, and 

 that at the same time it leads to results which, although not strictly accurate, 

 often give a very fair approximation to what is found in nature. 



If we decide provisionally to admit this conception, it is clear that we 

 may exclude from the generalised space all regions in which two spheres 

 intersect, or of course in which one sphere intersects the boundary, and 

 may suppose that when a collision occurs, the representative point in the 

 generalised space moves along the boundary of the excluded region, exactly 

 as in 35. In fact we may, in calculating the " effective molecular density " 

 regard the molecules as the rigid spheres of Chapter IV., the diameter of the 

 sphere of molecular action now being identical with the diameter of the 

 actual molecule. 



At the same time it is important to notice that the assumption of a 

 sphere of molecular action leaves very much more freedom for the structure 

 of the molecule than does the assumption that the molecules are elastic 

 spheres. For after assuming the existence of a sphere of molecular action, 

 it is still open for the molecule to have any shape we please: all that is 

 required is that it shall not protrude outside its sphere of action. Also 

 its interaction with a second molecule may be of any nature we please : 

 all that is required is that the interaction between two molecules shall be 

 negligible so long as their spheres do not overlap. Lastly, consistent with 

 the assumption of a sphere of molecular action, a molecule may have an 

 internal structure as complex as we please. 



General Intermolecular Forces. 



83, Before leaving the questions of the present Chapter, let us examine 

 the problem of determining the law of distribution of velocities and co- 

 ordinates in a gas in which the assumption of the smallness of the inter- 

 molecular forces is not justifiable. Let us say that an encounter between 

 two molecules takes place as soon as the potential energy of the inter- 



