> 
257 
This problem has already been discussed by Botrzmann') and by 
Remncanum’), both of whom applied BorrzmanN’s distribution law to 
the deduction of the pressure from the equation of the virial, and 
by ORNsTeIN®), who used GiBBs’s methods of statistical mechanics. In 
this $ our treatment of the problem will be based upon the Bor.TzMANN 
entropy principle, and at the same time we shall obtain an expression 
for the BorrzMANN M-funetion for this case, while the BOLTZMANN 
distribution law for this case will also result. In $ 6 we shall 
conclude with a discussion of a system of rigid molecules of central 
symmetry, each with an electric doublet at its centre. — 
The reader is referred to Suppl. N°. 24a, $ 2 and 3 for a general 
exposition of the method which forms the basis of the present inves- 
tigation, and for an application of this method to rigid spheres of 
central symmetry exerting VAN DER Waars attractive forces upon 
each other. 
In the case now under discussion the macro-complexion must first 
be determined as in § 3 by the conditions laid down in (4). In order 
to be in a position, however, to write down the energy equation 
for the present problem it is necessary to know how many pairs 
there are amongst those molecules, the distances between whose 
centres lie between certain definite limits. We shall assume that we 
have to differentiate only between molecules within whose sphere of 
influence are no other molecules and those within whose sphere of 
influence one other molecule is present; that is, that molecules which 
have two or more other molecules witbin their sphere of influence 
are of such infiequent occurrence in those states of the molecular 
system which we shall consider, that we may entirely neglect their 
influence. This supposes that the force exerted by any molecule is 
appreciable only over a finite sphere of influence which is small 
compared with the space in which the molecules are moving. We 
assume that the elements, dv, which are taken to determine the 
macro-complexion (cf. § 3) are large compared with this sphere of 
influence. We now divide the radius of the sphere of influence, r, 
into a great number of equal elements dr,, dr,, ete., which are so 
small that we may neglect the change in the potential energy of a 
pair of molecules during a change equal to one of these elements 
in the distance separating them. We shall subdivide the »,, molecules 
contained in dv, dw, into 
1) L. BoLrzMANN. Wien Sitz.-Ber. [2a] 105 (1896), p. 695, Wiss. Abh. 3, p. 547. 
In that paper the general result is also applied to the special case of repulsive 
forces varying as Kr-5. 
2) M. REINGANUM. Ann. a. Phys. (4) 6 (1901), p. 533. 
3) L. S. Ornstein. Diss. Leiden 1908, p. 70 sqq. 
