737 



'dip = ipj dm^ -f tp, (fin^ 

 = rfmj + (fw, [...... (20) 



In connection with the above considerations the work done by 

 external forces amounts to : 



dA = — pdVz= — p {v^dw, 4- v.dm,;) .... (21) 



If we now apply the condition of equilibrium (5), we obtain, 

 making use of (20) and (21), 



^i-{-pVr='^,+pv, (22) 



This equation represents the condition of equilibrium for the two 

 phases in the case considered here. 



4. Let us now imagine that the system consisting of the two 

 phases undergoes a real, infinitesimal change. The condition of 

 equilibrium f22) will then retain its validity. It is clear that it will 

 give us then a connection between the differentials of the variables. 



As variables determining the state, we choose for the solid phase the 

 dilatations and distortions x^, yy, z., y., z^, .%, besides the tempera* 

 ture T, for the liquid phase the volume v and the temperature T. We 

 ascribe the value zero to the variables Xx, yy, z^, y~, 2^^, and Xy in the state 

 from which we start (which, however, need not be without tension). 

 In order to be able to distinguish the difference between an eventually 

 ultimately reached final condition (which need not differ infinitely 

 little from the initial condition in mathematical sense) and the initial 



« 



condition from an actually infinitely small change of condition, we 

 shall represent the latter by dxx, dy^, dz~, dyz, dzx, dxy instead of by 

 ^^x, yy, Zz, yz, Zx, ocy, which we shall use for the final condition that is 

 eventually to be reached. This does not alter the fact that the latter 

 quantities are always treated as if they were infinitely small. 

 Proceeding in this way we obtain by differentiation from (22) t 



-— dJ -\- -^- dxx-{- ^-dyy\- --- dzz-\- v— ^^3/5 + t" dzx + 

 oT oxx oyy oz. oy. ozx 



+ ^— d^y + pdv, + v,dp =~—dT-\--—-dv,-\- pdv^ -f v^dp 



OXy 01 OV^ 



(23) 



In this ^-^ dxx denotes the increase of the free energy ^^, when 



OXx 



the initial state undergoes a dilatation dxx etc., just at this was the 

 case in (3) and the following formulae. 



Now according to the theory of elasticity we haVe: 



49* 



