404 -/ W. Gibhs — Equilihriurn of Heterogeneo^is /Substances. 



e — t?) -\- pv — //„ m„ — /.I,, tn,, — etc. — /u^ m„ — /j,, m,^— etc. =: ff s. 



Now if the value of G is negative, the value of the first member of 

 this equation will decrease as s increases, and may therefore be 

 decreased by making the mass to consist of thin alternate strata of 

 the two kinds of homogeneous masses which we are considering. 

 There will be no limit to the decrease which is thus possible with a 

 given value of v, so long as the equation is applicable, i. e., so long 

 as the strata have the properties of similar bodies in mass. But it 

 may easily be shown (as in a similar case on pages 131, 132) that 

 when the values of 



t, />, Ma, Ml., etc., M,, Mi, etc. 

 are regarded as fixed, being determined by the surface of discon- 

 tinuity in question, and the values of 



f, //, m^, m,,, etc., m,j, m,,, etc. 



are variable and may be determined by any body having the given 

 volume V, the first member of this equation cannot have an infinite 

 negative value, and must therefore have a least possible value, which 

 will be negative, if any value is negative, that is, if (f is negative. 



The body determining f, ?/, etc. which will give this least value 

 to this expression will evidently be sensibly homogeneous. With 

 respect to the formation of such a body, the system consisting of the 

 two homogeneous masses and the surface of discontinuity with the 

 negative tension is by (53) (see also page 133) at least practically 

 unstable, if the surface of discontinuity is very large, so that it can 

 afibrd the requisite material without sensible alteration of the values 

 of the potentials. (This limitation disap]>ears, if all the component 

 substances are found in the homogeneous masses.) Therefore, in a 

 system satisfying the conditions of practical stability with respect to 

 the possible formation of all kinds of homogeneous masses, negative 

 tensions of the surfaces of discontinuity are necessarily excluded. 



Let us noAV consider the condition which we obtain by applying 

 (516) to infinitesimal changes. The expression may be expanded as 

 before to the form (519), and then rediiced by equation (502) to the 

 form 



s{g" -G')+ «.f (/// - //;) + mf iiA,:' - n,!) + etc. 

 That the value of this expression shall be positive when the quanti- 

 ties are determined by two films which differ infinitely little is a 

 necessary condition of the stability of the film to which the single 



