( 537 ) 
d To) En. 
Ze aoe: De w (w de) (dn,_, + dn,4,) — 
—~ On, dn, QD yts5 dnt, 
ae oe » dz SATS eran Vir" 
pa dn, DE 4 G ) (= Az mal ee ) 
dz, 
Now we ¢an easily show that this sum is essentially negative. 
For this purpose we arrange the terms in the following way. From 
the first sum we take the term dn, yw (p dz) dn,—,, and also the ter m 
dn, —,wW(v dz) dn,. These are equal, and their sum is 
»y 
AS dn, On,—, W (v de). 
dz 
Next from the second sum we take the term 
dn, dn, dus 
— ——_—__— wp (v de), 
dv, AZ gy 
and also the term 
OR 2 5005) 00s 
— —- —ap (vp dz). 
dns dz, 
dys 
Adding those four we find ‘ 
beds doc, dn, Ors 
EN —— a | rde). 
dede dee, du, (cine 
dz, Ha) 
dn ' 
This result is essentially negative, for-— has the same sign at all 
points. *). 
We can arrange all the terms of (VII'") in the same way. Accord- 
ingly, the whole sum may be written as a sum of essentially 
negative quantities, and therefore d°‚log& is essentially negative. 
From this it follows that a system consisting of two coexisting phases 
with a capillary layer between them is stable, if the homogeneous 
phases taken by themselves are stable. 
$ 6. I shall now determine the entropy aid the free energy of 
the system considered. 
GiBBs®) showed that 4, the constant in the equation (IL) has 
1) A similar transformation does not hold for the elements of the homogeneous 
dn . 
phases for there EE = 0. 
2) J. W. Gress. Elementary principles in Statistical Mechanics 1902, 
