V36 



hydrostatic pressure will prevail everywhere in the liquid. We direct 

 our atlention to a part of the system that contains a portion of the 

 boundary plane between the solid and the ii(iuid phase. We assume 

 the surface that bounds the considered part of the system, for so 

 far as it falls inside the solid phase, to be invariable of position, 

 whereas we can subject it to variations of form for so far as it 

 falls inside the liquid phase. On this latter part acts then everywhere 

 the vertically directed hydrostatic pressure p. We take tlie part of 

 the solid phase that falls inside the considered part of the system, 

 as homogeneously deformed. 



Let the considered part of the system contain ?«i unities of mass 

 of the solid phase," m^ unities of mass of the liquid phase. The 

 direction of the normal to the boundary plane, which points from 

 the solid towards the liquid phase, may be called N. 



For (he part of the system in question are the free energy, the 

 mass, and the volume resp. : 



\\) = m^ if^, 4- vi^ V'2 1 



M = m,-\-m^ [ (19) 



V = mj7', + m^v^ I 



when Vj and i\ represent resp. the volume of the unity of mass 

 of the solid and the liquid phase. 



We now subject this part of the system to a virtual change. For 

 this purpose we make a small quantity of one phase pass into the 

 other at constant temperature. This will be attended with a change 

 of the total volume of the considered part of the system. In virtue 

 of the suppositions made above this change of volume can only take 

 place through the change of position of that part of the surface 

 bounding the considered })art of the system, which lies in the liquid 

 phase. For the rest the state of the liquid phase will not change. 

 In order to keep also the solid phase in the same state, to leave 

 the quantities determining the deformation unchanged, it will be 

 necessary, to make the tensions of the part of the boundarj^ surface 

 of the considered part of the system lying inside the solid phase 

 undergo intiiiitesimal variations. Since this part of the boundary 

 surface remains unchanged, no work will be required for this. The 

 only quantity of external work that we have to take into account, 

 will be that which is attended with the change of the part of (he 

 boundary surface lying inside the liquid phase. 



When dm^ and dm^ represent the changes of the quantities of the 

 two phases, then on account of (19), we shall have; 



