Physics. — "7\no theorems concerning the second r^irlal coefficient 

 for rigid .i-pherical molecules luhich besides collisional forces 

 only ed'ert Covi.OMB-forces and for which the total rharqe of 

 the active agent is zero", liy Ur. W. H. Kkksom. Sui)plement 

 No. 39/; to the Comiriuiiications from the Physical Laboratory 

 at Leiden. (C-omriiunicated by Prof. H. Kameki.ingh Onnes). 



(Communicated in tlie meeting of October 29). 



§ 1. In calculating the second virial coefficient B in the equation 

 of state written in the form : 



pt, = R7' (1 +- + - + .. .) (1) 



V V 



for a system of rigid spherical molecules, which carry a doublet at 

 the centre (Suppl. No. 24/», June 1912), the second term in the 

 development according to inverse powers of the temperature: 



B = B^(l+'^+p^ . . .) (2) 



did not occur. Tliis was also the case as regards all the higher odd 

 powers. 



In treating rigid spherical molecules which carry a quadruplet 

 of revolution-type in Suppl. No. 39^ (see p. 636), the second term in (2) 

 was again found to be absent, but in this case the higher terms 

 with b, etc. were present. 



The question now arises whether general conditions can be given 

 for the structure of the molecules under which the second term 

 in (2) does not occur. 



If, as will appear to be the case, such conditions can be given, 

 the next question is : can still further conditions be given under 

 which, if also satisfied by the molecules, no one of the odd powers 

 of r-i occurs in (2)? 



In discussing these questions we shall place ourselves completely 

 on the basis of classical mechanics. 



In that case the following theorems can be pi'oved : 



J . In the development of B the term with 7'-i does not occur 

 if the following conditions are fulfilled : 



(.4). a. the molecules behave at their collisions as rigid spheres, 



b. the attractive or repulsive forces ^), which the molecules exert 

 on each other, originate from fixed points in the molecule, and can 

 be derived from a Coulomb law of force (inversely proportional to 



'j Not including the collisional forces. 



