(154) 



in which one of the components occurs in the solid phase, though in 

 the extreme case it can be exceedingly small (i. e. practically 

 equal to zero), yet in general can never be rigorously equal to zero. 

 In this way the continuity remains preserved, and we may gi^e all 

 possible values to the cpiantities /? and /5' — as to /i' from to oo. 



We shall observe here at once that the quantity which dominates 

 the whole phenomenon is the quantity /J' of the solid phase. When 

 this quantity has a high value, the solid phase will contain only a 

 very small trace of one of the two components, and only when the value 

 of this quantity becomes comparable with the corresponding quantit}^ 

 /i in the liquid phase, the case of fig. 2 can occur. It is therefore 

 of the highest importance to know the exact signification of these 

 quantities /? and ^', or rather of the quantities « = '7i/? and «' = ^-j /3'. 



From the above deductions appears ]ianiely that the (piantity ca;"^ 

 does not represent anything else but the absorbed latent I teat \'QqmYQ(\ 

 for the mivimj per Or. Mol. for the case that an infinitely small 

 quantity of one of the components is mixed with the solution in 

 which the uiixing-proportiou for this component is I — x. h\ 

 the same way the quantity « (1 — xf represents the latent heat 

 for the other component in this solution. The quantity « itself is 

 therefore the latent heat for the first component for ,i' rrr 1 ; i.e. for 

 the case that the first component is mixed with a solution which 

 consists exclusively of the second component — or we may 

 also say that « is the latent heat for the second component for 

 a?=:0; i.e. for the case that this component is mixed with a solu- 

 tion consisting exclusively of the first. The fact that these two 

 quantities of latent heat are the same is a consequence of our 



.supposition h^ = b^, from which follows that a^ = — is equal to 

 «« = . In reality these two quantities will not alwavs be equal. 



2^1 



That the signification we have ascribed to the quantities a,v^ and 

 « (1 — ,vy is the true one, may be shown from the numerators of 

 equation (2), Avhich being respectively multiplied with q^ and q^, 

 represent the total latent heats of liquefaction n\ and u).^, namely 



w^ = 7, (1 + ^.v^ — ^'.v") — q.-t «.!•' — n.v'^ \ 



IV, =: q.^ f 1 + ^ [/J (1-.;)-^ - /i' {l-''r\] = 'h + « (l--'0^ - «' i^'-^O" I 



The total latent heat required for the liquefaction is therefore equal 

 to the 2>u^^ latent heat of liquefaction, augmented with the latent heat 

 required for the mixing of the liquid phase, diminished with that 

 required for the mixing of the solid j)hase. 



