THE CONTROL OF THE FACTORY. 



Another inferential control of the weights is obtained by the use of the 

 following equation 



Canes -f water = mixed juice -f megass ; 



data for solution of this equation can be obtained from the ordinary routine 

 analyses and one measurement as under. 2 Let / be the fibre in cane, m be 

 the fibre in megass, B c , Bj, Bm be the degrees Brix respectively of the absolute 

 juice, mixed juice, and residual juice in the megass. Let the weight of canes 

 be unity and the weight of the mixed juice be a; from well-known equations 



the weight of raegass is and the weight of the juice in the megass is (1 m). 



The total weight of juice is then a -\ (1 m). The solids in the total 



weight of juice then are 



a BJ +-/.(! - W ) B m 



M 



and the total solids per unit of juice are 



a Bj +-/-(! _i) B m 



-m) B m 



am + / ( I m) 



The water added per unit of original juice in the cane is then 



B c - a Bj m + / (1 - m) B m 

 _ a m -f- f (1 m) _ 

 a Bj-m + f (lm) B m 



a m -\- f (1 m) 



_a B c m -f / B c - f m B c - a Bj m - f B m + / m B m 

 a Bj m + / B m - f m B m 



Let this expression be denoted by P. The weight of original juice is 

 1 /; hence the total weight of added water is (1 f) P. Hence from the 

 equation 



Canes -f- water = mixed juice + megass 



A numerical example will show the application of this equation. 

 The following analytical data (expressed per unity) were found : 

 B c -209 (i.e., 20-9 Brix) ; / '119 ; m '487 ; Bj -190 ; B m '088 ; hence 

 -2443 and 1 -/= '881. 



From these quantities P is found to be 



00930 + -0074 



09250 + -0054 

 Whence 



,-00930 + -0074 X 



1 + -881(- - ) =a+ -2443. 



V-09250 + -0054' 



499 



