454 J. W. Gibbs— Equilibrium of Heterogeneous Substances. 
By differentiation of (24) and comparison with (23), we obtain 
d 
o=— 7 dt—I, du,—I, du, — ete., (26) 
: 7& me m3 
where 7s, Ij, I, ete. are written for +, —, s ete., and de- 
note the superficial densities of entropy and of the various sub- 
stances. We may regard a as a function of 4, 4, f, ete., from 
which if known 9s, I}, Ij, etc. may be determined in terms of 
the same variables. An equation between a, ¢, 44, / etc. may 
therefore be called a fundamental equation for the surface of dis- 
continuity. The same may be said of an equation between é*, 
wf, 8, m8, m§, etc. 
It is necessary for the stability of a surface of discontinuity 
that its tension shall be as small as that of any other surface 
which can exist between the same homogeneous masses with the 
same temperature and potentials. Beside this condition, which 
relates to the nature of the surface of discontinuity, there are 
other conditions of stability, which relate to the possible motion 
of such surfaces. One of these is that the tension shall be posi- 
stability or instability of the system are easily found, when the 
temperature and potentials of th 
as well as the fundamental equations for the interior mass an 
2=(p'-p)n (2) 
would be in equilibrium with a surrounding mass of the first 
phase. This equilibrium, as we have just seen, is instable, when 
the surrounding mass is indefinitely extended. A spherical 
