741 



position, so tliat no work will be done by external forces. The 

 condition of eqnilibrium is now : 



Ö W% . (40) 



We mnst use here the double sign seeing that there is only a 

 conversion possible in one direction. The sign = will hold for the 

 boundary equilibrium, i.e. the equilibrium at which a transition from 

 the solid to the liquid phase will just be possible. Now the equations 

 (35) give fui'ther 



dm, -4- öm„ =: ) 



J, . . (41) 



ni^6i\ + i\öm^ + m^6i\ + i\dm^ 1= ( ' ' 



in addition we have 



1 

 (iv, =z — (fz, (42) 



If we limit ourselves to the boundary equilibrium we get from 

 (12), (35). (39), (40), (41) and (42) making use of the equation 



Z, — jjz=0 (43) 



V'l -ï-pv, = i\'^ + pv, . . • . . . . (44) 



Hence we get the same relation as condition of equilibrium between 

 solid and liquid phase as we had for the case that the two phases 

 were in contact. Therefore the conclusions about the lowering of 

 the freezing point will also be the same. Of course as pressure on 

 the solid phase mu,^t then be taken into account the hydrostatic 

 pressure, to which must be added that which is exerted by the 

 solid bodies which are on the solid phase. 



7. We shall now consider more closely the amount of the lowering 

 of the freezing point, in which we shall make use of the expres- 

 sion (32). To calculate this amount it is necessary to know the 

 relation between the quantities .iv ...//;... and the tensions Xx. . . Vz- . . 

 In the most general case, the quantities .r,, . . . y.- . . . being considered 

 as infinitely small quantities, we shall be allowed to assume a 

 linear relation of the form : 



X,. = «,i.f^ + a,^y,, + «.jc, + «,,y, -|- «,,c^ -f «,,.r,/ j 



in which 



(iik = «i< (46) 



will generally hold, because the tensions Xx . . . F~ . . . according to 

 (8) may be considered as the partial differential quotients of the free 



