Separation of Three Liquids by Fractional Distillation. 13 



d£ _ a£ 



" y '~~" dS + dv + dt" a£ + b V + ct' 



brj c£ 



V * "~ af + fy + tf ; V% ~ af+417 + cf 



Let 



2 a ^ 1 1 ^ .1 



/. f = Ls*+ 1 , t? = M> +1 , £=N* ; 

 .-. 1-* = % +v+£ = L^ + M^+i+Ns ; 



yi == aL^ + bMzP + cN'' y * " = aLe* + 6M> + cN ; 



2/3 ~ aL^ + ftM^ + cN* 



The elimination of z from the expressions for x and y is 

 impracticable, but the curves may be readily traced by treat- 

 ing z as an independent variable. 



In the following curves (figs. 4 & 5) we have taken 



a = 4, b = 2, c = l, [and .*. \ = 3, ^=1], 



these being nearly proportional to the vapour-pressures of 

 methyl, ethyl, and propyl acetates. 



I. represents the first distillation ; in it L = M = N=^. 

 II. a, II. /3, II. 7, II. 8, II. e represent what would take place 

 if the five fractions into which I. is divided were separately 

 distilled ; the composition of these fractions being found from 

 the curves I. to be : — 



A or L. B or M. C or N. 



II. a -543 -300 -157 



II./3 -47 -33 -20 



II. 7 -37 -365 -265 



II. 8 -22 -39 -39 



II. e -047 -265 -687 



