THERMODYNAMIC AL SYSTEM OF GIBBS 



159 



ordinate of E' is i; -{■ (m — mOAws or f + /x2A?n2 + miAwi, 

 since Atwj = —Ami. If Af > n^^m^ + miAwi, the point E is 

 above the point E'. Therefore the condition of stability of the 

 phase D, with respect to continuous changes, is that the f-curve 

 for adjacent phases shall be above the tangent at D, except at 

 the single point of contact. 



nig'O 



Trt^'l 



Fig. 7 



33. Conditions with Respect to Temperature and the Potentials. 

 Since (213) holds true of any two infinitesimally differing phases, 

 within the limits of stabiHty, we may combine this condition, viz., 



rj"{t" - t') - v"{p" - p') + m,"W - Ml') 



. . . + mn"{lXn" - fin) > 0, 



and the condition obtained by interchanging the single and 

 double accents, i.e., 



V'it' - t") - V'(p' - p") + W/W - Ml") 

 . . . + m„'(Mn' - Hn") > 0, 



