Properties of a Mixture of Liquids. 403 



"p 

 Let us then substitute s= -rkq 1 " m equation (11) and inte- 

 grate : we have now in all three constants (including the one 

 introduced by integration), and two boundary conditions 

 (2? = 7Tb when q = 0, p — ir^ when q = co), so that one constant 

 remains to be determined by experiment. 

 Equation (11) becomes 



Br Bkrq<- i Igp 



Bq + A Bktf + A'*' p-dv J ' ■ ' K } 



which, integrated, is 



rlogf q * j-log(Bfy r + A)+log j p = const., . (17) 

 and by introducing the boundary conditions, we obtain 



(Bg + A)' ^ (18) 



with 



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But as 



f/yf- 



B , B'Q'7r A 

 s= —kqr=z — r-2 



A * A r 7T B ' 



we have, as in the preceding case, the partial pressures repre- 

 sented by the two terms of the equation ; or 



^(b^a)^' ^Kb^Ta)*^- • • (20) 



With regard to equation (18) it is to be noted : 1st, that (14) 

 is a particular case of it, with r=l ; 2nd, that when r=Q the 

 pressure of the mixed vapour is the sum of the pressures of 

 the two pure substances ; that is the case when the two 

 liquids do not mix ; 3rd, that when r has any other (positive) 

 value the function has a maximum or minimum. To find 

 this we must put "dpfdq = 0, or (considering the numerator of 

 the differential coefficient only) 



B r <7r x rq r ^{Bq + A)**- (B r w A q r + A r irn)r{Bq + A^B = 0, 



whence 



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