( 533 } 
§ 4. Before Ll proceed to the discussion of the stability I shall 
consider the equation (VI). Using (6’) we can put for it 
oo 2 at d log w, a dans Zeer vr" 
og — + n, ——— —— — —_=f.. ... 
9 Dz dn, 7) 7) ie \ 
Subtracting the equation (VI) taken for the height z, + dz, from 
the corresponding one relating to the height z, we obtain 
1 d log w, d? log w, 2a dn, 2 de, 
—— +2 zn 1, ——— SS) BRE 5’ 
is dn, ane © / de, © dz, 
If we introduce the function p, determined by the equation 
P 
— = 1h —" 1" 
6) dn 0) 
dlogw an’ 
yh Ott EE 1 
— which quantity represents the pressure in every element of a 
homogeneous system with the molecular density n — we easily see 
that we can replace (7) by 
1 dp, dn, 2 der 
On, dn, dz, @ dz,” 
This equation leads to 
dn, de, 
hg AE 5 
dz, dz, 
The form of this relation recalls the statistical condition of equili- 
brium namely that the difference of pressure between two planes 
be equal to the force acting on the mass between these planes. 
By integrating (9) from a point of the homogeneous phase (indi- 
cated by the index A) to a point of the capillary layer (index x) we 
find 
cd 
ex ao 
dt 
de, dn 
Ph — px =2 tn a, dz = Oren — 2 = ec dz, 
& az 
mh Zh 
d2sn 
we have avoided to prove for each of the integrals fnò 7 zes d2 separately that 
d 22 
d?sn 
we can put for i on te dz, as is done in the treatise of van pER Waats— 
Kounstamm p. 238. 
In the paper of van per Waats this gives something accidental to the appearing 
of €, in the condition (VI). This advantage is due to the fact that the hypothesis 
of continuous transition and the expansion «, in a series have been introduced 
after the deduction of the condition (VI). 
