( 536 ) 
d d log Wy Zan, dn*, 
dz lo c= —1+4 n*,, ——— F 
ae ( zl dn, ) + 7) ) De 2n, 
ha 
where @ is 1 or 2. These contributions are negative, if 
d , dlog os 2an, 
net aken Bree Mare feos re a A 
Now, we can transform this condition by means of the function p 
(c. f. (8)). We then find as a condition for the stability 
Re 8 eo 
for the homogeneous phases. As for these phases, the function pz 
represents the pressure, the condition (IX’) is nothing else than the 
known thermodynamical condition for stability. 
Not only must (IX) be fulfilled, it is also necessary that d*,log§ 
be negative, for there are possible variations in which du, is zero 
everywhere in the homogeneous layers. 
I shall transform the first sum in d° /og§ by means of (VI). I 
shall write for it 
~ dn, 1 1 od d log w, 
. dn, | — — + = cg og ; 
2 ny n, dn, dr, 
c 
which may be replaced by 
dn, d , d log w, 
Sr: tn (tay 2 ii **) 
c 
By a transformation of the same kind as that which leads to 
(7), we can replace the foregoing expression by 
dé, 
| = dz: 
J x J ek 
0) pS ig dn, 
dz, 
Introducing the value of ©, by means of (5'), and considering that 
the differentiation of n,—, with respect to z, gives the same result 
as that with respect to z,_,, we find for the sum under consideration 
a dz dn dn, ane. Gas 
== Sige as Sw (vdz i) Ke 
GO ef dn, hae pine) dE ae dze 
dz 
therefore (VII) may be reduced to 
