CANE SUGAR. 



Algebraical Theory of Sugar Boiling. 



Let x =^ Brix of the massecuite.* 



s =. solubility of sugar in the mother liquor or molasses. 

 p = purity of the massecuite. 

 m = purity of the molasses. 

 Then (1 x} = water in the massecuite. 



* (1 x) sugar in solution, i.e., in the molasses. 

 x (1 p) = total non-sugar or impurities. 



(For convenience of calculation these purities are referred to unity 

 instead of to 100 as is usual.) 

 Then 



_ * (* *0 



~- 8 (\-x) + (\-p) x 

 and 



ms 



x 



8 -f- m ms mp ^ 



Let there be two massecuites of different purity, both boiled to the same 

 degree Brix, the solubility of the sugar in the mother liquor remaining the 

 same ; then as p increases \-p decreases, and the denominator in the expression 

 (1) decreases, so that the value of m increases. 



It follows then that as the purity of a massecuite increases, so also 

 increases the purity of the mother liquor provided that the Brix to which the 

 massecuites are boiled remains the same. 



In the table below are calculated values of the expression : 



(!*) 



s(l -x) + (lp)x 



for values of x = '90, s = 2'0 and p = 75 to 95, connecting purity of masse- 

 cuite and purity of resulting molasses when the Brix of the massecuite is 

 constant at 90 and solubility of sugar in molasses is 2*0 



In what follows Brix is here used as synonymous with true total solids. 



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