368 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



The term a-s represents the work spent in forming the surface, and 

 the term (p"p')v" the work gained in forming the interior 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 affording a kind of measure of its 

 stability. We may easily express the value of W in a form which 

 does not involve any geometrical magnitudes, viz., 







> 



where p", p' and cr may be regarded as functions of the temperature 

 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 con- 

 clusions are all, however, practically limited to the case in which 

 the value of r, as determined by equation (27), is of sensible 

 magnitude. 



With respect to the somewhat similar problem of the stability 

 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 denoted 

 by A, B, and C ; their pressures by p A , p E and p c ; and the tensions 

 of the three possible surfaces by o- ABJ O"BC> OAC- If PC i s I GSS than 



there will be no tendency toward the formation of the new phase 

 at the surface between A and B. If the temperature or potentials 

 are now varied until p c is equal to the above expression, there are 

 two cases to be distinguished. The tension 0- AB will b e either equal 

 to O- AC + <TBC or l ess - (A greater value could only relate to an unstable 

 and therefore unusual surface.) If (r A B = cr A c+o-Bc> a farther variation 

 of the temperature or potentials, making p c greater than the above 

 expression, would cause the phase C to be formed at the surface 

 between A and B. But if OT A B < O"AC + O"BC> the surface between A and 

 B would remain stable, but with rapidly diminishing stability, after 

 p c has passed the limit mentioned. 



The conditions of stability for a line where several surfaces of 

 discontinuity meet, with respect to the possible formation of a new 

 surface, are capable of a very simple expression. If the surfaces A-B, 

 B-C, C-D, D-A, separating the masses A, B, C, D, meet along a line, 

 it is necessary for equilibrium that their tensions and directions at 

 any point of the line should be such that a quadrilateral a, /3, y, S 

 may be formed with sides representing in direction and length the 

 normals and tensions of the successive surfaces. For the stability 



