78 The Law of Distribution [CH. v 



In general, for the multiple molecule a/rty ... we have 



> ............ (187). 



86. From the well-known formula in attractions 



where p, V are density and potential at the point x, y, z, it follows that we 

 can write W a in the form 



where % a is the potential of the molecule of type a. in the field of inter- 

 molecular forces arising from the other molecules, and so on. Hence in 

 equation (187) we may write 



<0y... = ^a^^y ........................... (188), 



where ^ a = Ae- zhE - h *, etc ................... (189). 



We may therefore regard the probability of a combination of molecules 

 having any specified coordinates, as the product of the probabilities of the 

 constituent molecules having the appropriate coordinates, if we take the 

 probability of a molecule of type a having its coordinates within the usual 

 range d^d^ ... to be 



Ae-to^-Kid&dl;, ........................ (190). 



Since the quantity % does not involve the velocity coordinates it is clear 

 that the analysis of 77 can be made to apply to this case, and hence that 

 the result expressed by equation (161) is true, even when intermolecular 

 forces are taken into account. Thus we see that the law of distribution of 

 velocity-coordinates is unaltered by the presence of intermolecular forces, and 

 that the law of equipartition of kinetic energy remains valid independently 

 of the existence of such forces. 



87. Before leaving the subject we must notice the similarity between 

 the effects of an intermolecular and an external field of force. If ^ a instead 

 of being the potential of a molecule type a in an intermolecular field of 

 force, had been the potential in a permanent external field of force, then the 

 law of distribution of molecules of type a. would, by 75, be exactly the 

 same as that expressed by (190), except that ^ would have been replaced 



