1322 
Toy dV, A ford Ve Ie: he ab (TP 
The coëfficients pk etc. indicate the asitishas of the elements. 
In a homogeneous phase they will only depend on the distance 
between the elements, whereas in a capillary transitory layer the 
function will be different. 
As we published our paper we met with difficulties in the kinetic 
deduction of formula (1), owing to the fact that we tried to work 
with mathematically infinitely small elements of volume. As Dr. 
ZERNIKE') has now solved another difficulty adhering to our con- 
siderations it is worth demonstrating that a deduction from statis- 
tical mechanics of (1) is possible. [n this way it will be possible to 
indicate the physical meaning of function f and to prove that [fd V 
taken with respect to the working sphere is at the critical point equal 
to unity, which formerly was demonstrated by an artifice. 
Starting from (12) of the cited paper the proof of formula (1) 
is very simple. 
The number ‘of the systems (3), for which in the elements dV- 
and dV, the deviations of the mean number of particles amount to 
vy, and», was found to be: | 
1 be Ad alos 
NO Os Aen al (- i C 0? og W Poo ) pe 
S= Cwrg” 2e 5 yv v do do OdV if 
VP 
. PP ot = 2 
te Pai (2) 
In this formula 9 represents the number of molecules per unit 
. n . . . ; 
of volume 6} Pe is the mutual potential energy for a couple of 
molecules the one of which is lying in the element eg, the other in 
the element t, w is the function defined in my Thesis. 
Now considering that the quantity tie) or By dik as appears from 
the equation of state) is of the order of the unity, every term of 
the form 77 
Ody 
will be small with respect to unity. Hence we may 
develop in the exponential function the part containing in v- and 
v, and write (summarising unimportant terms in the constant D): 
Wee ae , dlog 
¢—D 2, (— Pe ante do ) #7 1 Poor Pas 
= ANG S ee : ; 
( +o zer = ap) 6) 
!) The clustering tendency of the molecules in the critical state and the extinction 
of light caused thereby. These Proc. XVIII, p. 1520. 1916. 
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