200 ./ W. Gihhs — Equilibrium of Heterogeneous Substances. 



ponents. The phases in question are those for which 7/ is a maximum 

 for constant values of £, v, w„, . . . m,, ; or, as they may also be 

 described, those for which e is a minimum for constant values of ?;, v, 

 m„ . . . ni,, ; or for which 'Q is a minimum for constant values of 

 t, p, m„, . . . m,,. The phases which satisfy this condition may be 

 readily determined when the fundamental equation (which will con- 

 tain the quantities m^, . . . ni„ or yWj, . . . //„,) is known. Indeed it is 

 easy to see that we may express the conditions which determine these 

 phases by substituting /<j, ...//„ for the letters denoting the units 

 of the corresponding substances in the equations which express the 

 equivalence in ultimate analysis between these units. 



These phases may be called, with reference to the kind of change 

 which we are considering, phases of dissipated energ}^ That we 

 have used a similar term before, with reference to a diiferent kind of 

 changes, yet in a sense entirely analogous, need not create confusion. 



Tt is chai-acteristic of these phases that we cannot alter the values 

 of wij, . . . Wn in any real mass in such a phase, while the volume of 

 the mass as well as its matter remain unchanged, without diminish- 

 in o- the energy or increasing the entropy of some other system. 

 Hence, if the mass is large, its equilibrium can be but slightly dis- 

 turbed by the action of any small body, or by a single electric spark, 

 or by any cause which is not in some way proportioned to the effect 

 to be produced. But when the proportion of the proximate compo- 

 nents of a mass taken in connection with its temperature and pressure 

 is not such as to constitute a phase of dissipated energy, it may be 

 possible to cause great changes in the mass by the contact of a very 

 small body. Indeed it is possible that the changes produced by such 

 contact may only be limited by the attainment of a phase of dissipated 

 energy. Such a result will probably be produced in a fluid mass by 

 contact with another fliiid which contains molecules of all the kinds 

 which occur in the first fluid (or at least all those which contain 

 the same kinds of matter which also occur in other sorts of molecules), 

 but which differs from the first fluid in that the quantities of the 

 various kinds of molecules are entirely determined by the ultimate 

 composition of the fluid and its temperature and pressure. Or, to 

 speak without reference to the molecular state of the fluid, the result 

 considered would doubtless be brought about by contact with another 

 fluid which absorbs all the proximate components of the first, 

 S ... aS'„, (or all those betw-ien which there exist relations of equiva- 

 lence in respect to their ultimate analysis), independently, and with- 

 out passive resistances, but for which the phase is completely deter- 



