265 
spheres of central symmetry, each having at its centre an electric 
doublet ; we shall assume that the distance between the two poles 
of the doublet is negligible compared with the dimensions of 
the molecule, while the moment of the doublet is nevertheless so 
large that it must be allowed for by introducing terms into the 
equation of state to represent the mutual action between the doublets. 
In all eonsiderations introduced into the present section we shall 
regard the moment of the doublet as constant. A model of a mole- 
cule which, in so far as its externa! action is concerned, could be 
regarded as approximating closely to such a doublet, would be given 
by a non-conducting sphere with a uniform distribution of positive 
electricity (or with the charge distributed in concentric shells, each of 
constant density) in which there is an immovable electron at a very 
small distance from the centre (the centre coinciding with the centre 
of gravity). The terminology of this section, however, will be chosen 
with reference to the supposition of two poles infinitely close to 
each other ‘electric doublet) at the centre of the sphere. External 
action will be calculated as if only electrostatic forces were invol- 
ved. In this supposition the mutual action of two molecules may 
be treated as being governed by the Hamitton equations. The 
assumption would have to be more closely verified in the further 
development of the theory of the action of a model such as the one 
just described. 
Van per Waars Jr.) has considered such a system as the one 
here described, and calculated the mean attraction between two 
molecules when these have assumed orientations with respect to the 
axes of the doublets which are in accord with the condition for heat 
equilibrium; he showed that the law of decrease of this attraction with 
increasing distance must be more rapid than r—4, 
The object of the present section is to deduce the virial-coefficient 
B by the method indicated in § 2. 
The group macro-complexion is first determined by (22) as in the 
treatment for smooth ellipsoids in $ 4. 
In order to be able to evaluate the potential energy it is necessary 
to subdivide the n, molecules present in the volume-element dv, 
into 7, single molecules (cf. § 5), and n,, molecules which belong 
to molecular pairs, and exert forces upon each other of such magni- 
tude that they must be allowed for in the determination of B. We 
shall once more assume that cases in which one molecule is acted 
upon by more than one other molecule with forces sufficiently 
1) J. D, van Der Waats Jr., These Proceedings June, Oct. 1908, March 1912. 
