J. W. Gibbs— Equilibrium of Heterogeneous Substances, 455 
mass a little larger would tend to increase indefinitely. The 
work required to form such a spherical mass, by a reversible 
process, in the interior of an infinite mass of the other phase, 
is given by the equation 
W=os—(p"— p')v’. (28) 
The term gs represents the work spent in forming the surface, 
and the term (p”’— p’)v” the work gained in forming the inte- 
rior mass. The second of these quantities is always equal to 
two-thirds of the first. The value of W is therefore positive, 
and the phase is in strictness stable, the quantity W afford- 
ing a kind of measure of its stability. We may easily express 
the value of W in a form which does not involve any geo- 
metrical magnitudes, viz: 
: 16z0° 
= SS 29 
3( p" —p' y ? ( ) 
where p”’, p’ and o may be regarded as functions of the tempe- 
rature and potentials. It will be seen that the stability, thus 
measured, is infinite for an infinitesimal difference of pressures, 
but decreases very rapidly as the difference of pressures 
increases, These conclusions are all, however, practically lim- 
ited to the case in which the value of 7, as determined by 
equation (27) is of sensible magnitude. ; 
_ With respect to the somewhat similar problem of the stabil- 
ity of the surface of contact of two phases with respect to the 
formation of a new, phase, the following results are obtained. 
Let the phases (supposed to have the same temperature and 
potentials) be denbund be A, B, and C; their pressures by pa, 
Pz and pc; and the tensions of the three possible surfaces o,s, 
%Bc, Fac. If pe is less than 
Oxc Pat FacPs 
Ope + Fac 
there will be no tendency toward the formation of the new 
phase at the surface between A and B. the temperature or 
potentials are now varied until p¢ is equal to the above expres- 
sion, there are two cases to be distinguished. The tension @,4, 
will be either equal to @4¢ + gc or less. (A greater value 
could only relate to an unstable and therefore unusual surface. 
FxB = Gx¢ + Ggo, a farther variation of the temperature or 
potentials, making p, greater than the above expression, would 
cause the phase C to be formed at the surface between A and 
B. Butif os, < xc + Oxo. the surface between A and B would 
remain stable, but with rapidly diminishing stability, after pg 
has passed the limit mentioned. hades tua 
? 
The conditions of stability for a line where several surfaces _ 
of discontinuity meet, with respect to the possible formation of 
