552 CHAPTER XXVII 



be the degrees Brix respectively of the absolute juice, mixed juice, and residual 

 juice in the bagasse. Let the weight of canes be unity and the weight of the 



f 

 mixed juice be a ; from well-known equations the weight of bagasse is -^ 



f 

 and the weight of the juice in the bagasse is — (i — m). 



f 

 The total weight of juice is then a + — (i — m). The solids in the total 

 ° ■■ m 



weight of juice then are 



f 

 a Bj + — (i — m) B„ 



and the total solids per unit of juice are 



/ 

 a Bi + — (i — m) B,n 



7 



« + — (l — w) 

 m 



a Bj m ~\- f {i — m) B^ 



~ a m -\-f {i — m) 



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



Be — a Bj m -\- f {i — m) Bm 



a m -\- f {i — m) 



a Bjfn -\- f {t — m) B^ 

 a m -\- f {i — m) 

 _ a Bg m +f Be —fm Bg — a Bj m —fBm -\- f m B^ 

 ~ a Bjin +f Bm — j m B^ 



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

 I — /; hence the total weight of added water is (i — /) P. Hence from the 

 equation 



Canes + water = mixed juice -\- bagasse 



I +(i -/)P-a+-^ . 



A numerical example will show the application of this equation. 



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



Be 0'209 [i.e., 20-9 Brix) ; / 0-119 ; m 0-487 ; Bj 0-190 ; Bm o-o88 ; 



f 

 hsnce ^^ = o • 2443 and i — / = o - 881. 



From these quantities P is found to be 



o* 0093a + 0-0074 



o- 0925a + 0-0054 



whence 



00 /o - 0093a + 0-0074\ 



I -f o-88i{ ^ — —)== ^ + 0-2443- 



Vo - 0925a + 0-0054/ 



Solving this equation a is found to be 0-91 15, or the weight of mixed 

 juice is 91-15 per cent, on that of the cane. 



The weight of bagasse is 24 '43 percent, on cane, so that, putting the weight 



