1313 
barer Weise abweichen von den Kigenschaften, die man durch Inter- 
polation zwischen Zuständen, die um den kritischen herumliegen, 
aber weiter von ihm entfernt bleiben, erwarten sollte.” 
KAMERLINGH ONNEs and Kerrsom assert to have found deviations 
pointing to suchlike causes and they have tried to account for the 
special phenomena at the critical point by adding a function of 
disturbance to the equation of state which takes specially large 
values in the critical point. 
In this contribution we will try to point out that there can be 
no question about a function of disturbance caused by the accidental 
deviations of density. 
In deducing the equation of state we will use the method of the 
virial. The virial theorem takes the form 
oF +2 (7, Xn + yk Vn + ende) d- DZ raz (rap) = 0 
if L is the kinetic energy, the coordinates of the molecules are 
Cho Yh, Zh, the distance between the centres of a pair of molecules 
h and k is rj, the external forces are X, VY; Zj, and the force 
between the pair of molecules h.k is F'(zjz). If the pressure is the 
only external force, the second average may be represented by 
— 3p V, whereas the average kinetic energy orde on the abso- 
lute temperature in the known way. *) 
We will now take into consideration the second sum. Suppose 
the volume V containing » molecules to be divided into a large number 
of elements dv;,; let the mean density in these elements be 9. Now 
consider a system in which the density in the different elements can 
be represented by o-+ ry. Then the contribution by the elements 
dv, and dv, to the sum mentioned above amounts to 
(0 + rx) (9 + va) Tae F (rat) dor dor. | 
By integrating this expression with respect to dv, and dr, over 
the volume V we get, passing to the mean values, twice the 
required sum. Taking the averages the terms ev, and or, will not 
contribute, the average of vj, = vz being zero. 
The contribution 
ffe F (rik) run dor dor, 
is the one taken into account by the usual theory, which neglects 
accidental deviations of density, and which therefore takes for @ 
the mean value, or what comes to the same, the most common 
value. Hence the correction for deviations of density appears to be 
1) Compare e.g. L. Botrzmann, Gastheorie II, p- 141. 
