1514 
ffe re rak F (rap) dor don. 
Now this integral can be transformed by means of the function g, 
which we have introduced into our considerations on the opalescence 
in the critical point. *) 
According to the definition of the function g, the mean value of 
pz if vj is kept constant may be represented by 
Ve Vp ATH) dor. 
Further we have shown that: 
VE VE = 9 (Tak) VA? dp, = 09 (TAK) 
(le; Pe (96), (8), 
Introducing this we get 
ffe rik FE (vn) 9 ak) dor don. a 
For this we may write 
n fru F (7k) g (rh k) dv 
as fo an represents the whole number of molecules. 
If we proceed to the usual first approximation regarding the terms 
of the first integral, then we find as equation of state : 
MLE & b 1 : 
Pa Eni, 1+ 7 + = mg (rk) +The» F (rag) dor 
v 
V 
where v= —, and m is the mass of the molecule. 
nm 
This formula shows that if we take into account the deviations 
of density, we find a new term in the equation of state. This term 
however is not equivalent to the function of disturbance of KAMERLINGH 
Onnes and KeesoM. The special character of the function g in the neigh- 
bourhood of the critical point causing the clustering tendency there 
to become very strong, consists in the fact that this function gets 
perceptible values for points far outside the sphere of action, so that 
= 
for the critical state lg dv does not converge any more. Pheno- 
0 
mena connected with this last integral become therefore specially 
strong at the critical point. For small values of 7, inside che sphere 
of action, g hardly changes when we approach the critical point ; 
and only these values have influence on the found term of correction. 
1) L S. Ornstein and F Zernike. The accidental deviations of density and the 
opalescence in the critical point. These proc. XVII, p. 793. 
