Z 
dn 
Carne, ee ret Gene) 
i. e. the free energy increases proportionally to the surface. Only 
the elements of the capillary layer contribute to the integrals, for 
dn 
it is only in these elements that « and = differ from zero. The 
quantities expressed by (17) and (18), taken with the negative sign, 
agree with what is commonly called the capillary energy. In this 
form they also represent the so called surface tension. 
The quantity 
Zx 
dn 
Ph — DrEcz + > sn e-dz, 
az 
Zh 
or the corresponding approximate quantity (c. f. (16)) 
A Cy de dn, 2 
5 a Eede (PL 
ee 2 i dz’, de 
may be called the horizontal pressure in the element dz, at the 
height z,. I shall represent it by pi. As we can see from (10), the 
connection between p‚and p„ is given by the formula 
Wig Yon, Ere LT ee MA 
The term e‚ being 0 in the homogeneous layer, we have 
Pix = Pr = Phi = Pho: 
We can determine the sign of &,, and therefore that of pu —- pr, 
by means of the equations (VI) and (10). We then come to a discus- 
sion exactly analogous to that which vaN DER Waats has given on 
p. 19 of his paper’). 
If one goes upward from the liquid phase, « is first 0, then 
positive, then O again, after that negative and finally O in the gaseous 
phase. 
By means of the foregoing considerations, we can obtain all the 
results formerly found by van ber Waats and the above method 
may also be applied to a spherical mass, whose density is distributed 
symmetrically around the centre. 
1) Cf. van DER Waats-—Kounstamu p. 239, 
