THERMODYNAMICAL SYSTEM OF GIBBS 153 



adjacent phases), we may apply to such changes the same 

 general test as before. It is evidently only necessary to con- 

 sider as the component substances of such phases the inde- 

 pendently variable components of the given fluid. The con- 

 stants Ml, M2, etc. in (201) have the values of the potentials 

 for these components in the given fluid, for which the value of 

 (201) is necessarily zero. Then, if for any infinitely small 

 variation of the phase the value of {201) can become negative, 

 the fluid will he unstable; but if for every infinitely small variation 

 of the phase {201) becomes positive, the fluid will be stable. Gibbs 

 points out that the case in which the phase can be varied 

 without altering the value of (201) can hardly be expected to 

 occur. For, in such a case, the phase concerned would have 

 coexistent adjacent phases. 



This condition, which Gibbs calls the condition of stability, 

 may be written in the form 



e" - t'r," + P'v" - ixi'm," ... - Mn'm„" > 0, (209) [142] 



where t', p', ni, m', etc. are the temperature, pressure and the 

 potentials in the phase, the stability of which is in question, and 

 t", 1]" , v", mi', rrii", etc., are the energy, entropy, volume and 

 quantities of the components in any adjacent phase. Single 

 accents are used to distinguish quantities referring to the first 

 phase, and double accents those referring to the second. 



Particular conditions of stability can be obtained by trans- 

 forming this equation in various ways. 



30. Condition with Respect to the Variation of the Energy. 

 If we add 



- e' -f t'r)' - p'v' + m'mi' + yii'nh' ... + Mn'w„' = 0, 



to (209), we obtain 



(e" - t') - t'{r}" - v') -h p'{v" - v') - uLi'{mi" - m/) 



-M2'(W - m') ... > 0, [143] 



which may be written in the form 



Ae > tAr) — pAv -f mAmi + HiAm2 . . . + UnAmn, (210) [145] 



