740 



This will also apply to the case that the initial state is not 

 tensionless; only (34) does not represent then the difference ^n 

 melting heat between the state x^ . . . yz . . . and the tensionless state, 

 but the difference between the state Xx---i/z-" and the initial state, 

 which is not tensionless in this case. 



' 6. Let us now suppose that forces act on the surface of the 

 solid phase which are exerted by solid bodies which rest on the 

 solid phase, and in consequence of the presence of which the sur- 

 face of the phase is not in contact with the liquid phase. We can 

 then imagine that a small part of the solid phase that is in contact 

 with the solid bodies which exert forces, is converted to the liquid 

 state, without the solid bodies changing their places. For this case 

 we can again draw up the condition of equilibrium. 



We take the boundary plane of the solid phase as XT-plane, and 

 suppose that the ^T-axis is the normal to this plane which is directed 

 from the solid to the liquid phase. For the total free energy, the 

 mass, and the volunie the following relations hold in this case: 



W = m, ip, + m, ip, 1 



M=zm^-{-m^ I (35) 



V:=z 7/ij Vj -f- Wj I'j ) 



Let now an infinitely small quantity of the solid phase be con- 

 verted to the liquid phase, then : 



d'F = m,ö^, + xi\öm, + m,öi]\ + tp.cJw, . . . (36) 



During the conversion the volumes v^ and v^ will have to change, 

 as the total volume remains constant, as we supposed. The considered 

 change being a virtual change, we may assume that as far as the 

 solid phase is concerned, this change is brought about by variation 

 of Zz alone. Then we get : 



(fi,,, = ^ . (f^, ........ (37) 



Further : 



öxp,= ^.öv, (38) 



Ov., 



By introduction of (37) and (38) into (36) we get: 



öW = m. ^-— * dz. m^ —^ 6v^ -\- \\>^öm^ -\- ipjdVn, . . (39) 



Just as before (see above under 3) the tensions at the surface that 

 bounds the considered part of the system will have to vary now 

 too. We supposed, however, that this surface does not change its 



