637 



No. 24 we treat as bodies of revolution as regards their fields of 

 force. So we are led to the problem to deduce the second virial 

 coefficient for a system of rigid spheres, whose attraction is ecpii- 

 valent to that of a quadruplet with two coinciding axes, and which 

 is obtained when two doublets are placed along the same line with 

 two homonymous poles towards one another and their distance 

 approaches zero with maintenance of a finite quadruplet-moment "'). 

 We place ourselves in this communication on the standpoint of 

 classical mechanics. The quantum theory only intervenes in so far 

 as the fact that according to that theory the rotations of a diatomic 

 molecide about one of its principal axes of inertia in consequence 

 of the smallness of the corresponding moment of inertia is not 

 influenced appreciably by the heat motion, is accounted for in our 

 treatment according to the principles of classical mechanics by 

 considering such a molecule as a body of revolution. We do not 

 consider here an influence, as given by the quantum theory, on the 

 rotations about the two other principal axes of inertia nor a possible 

 influence on the translational motion. If perhaps the bearing of the 

 results obtained in this paper is liuiited by this circumstance, still 

 they are in any case applicable to molecules for which these two 

 principal moments of inertia and eventually the molecular weight 

 in connection with the temperature region which is to be considered 

 are sufficiently large. 



§ 2. As we explained in § 1 we will consider hero the molecules 

 as rigid s|)heres of concentric structure "), with at their centre a 

 quadruplet which consists of two doublets whose axes lie in the .same 

 line and have opposite directions, and which approach each othei' 

 indefinitely preserving, however, a finite quadruplet-moment. 



For calculating the second virial coefficient we have again to 

 consider, just as in Suppl. N°. 24 a and b, pairs of molecules which 

 at a given moment lie in each other's sphere of action. The nuitual 

 position of a pair can be specified in a way corresponding to that 

 followed in Suppl. N°. 24è § 6 in discussing the doublets, \ iz. by 

 the following coordinates (Fig. 1): 



1^'. the distance r between the centres; 



1) J. G. Maxwell. Electricily and Magnetism. 3rd ed. Vol. I, p. 197. 



-) This expression is meant to indicate that the density is uniformly distributed 

 over concentric spherical layers. Yet the following deduction of B is also valid 

 if the density is distributed symmetrically about an axis, if this axis coincides 

 with the axis of the quadruplet. The result is, as far as regards 5, even more 

 general and is also valid, if the density is distributed arbitrarily. 



