238 CHAPTER XI 



The Economic Limit of Extraction. — In schemes employing the addition 

 of water, expense is frequently incurred in the evaporation thereof, though 

 often the fuel afforded by the bagasse is sufficient to treat considerable 

 quantities of water. In what follows the factory is supposed to be balanced 

 when dry crushing is operated ; that is to say, under these conditions the 

 bagasse just suffices for the operation. All expenses then connected with 

 imbibition are to be charged to the debit side of the ledger. 



Let there be unit quantity of juice (or of sugar) in the dry crushed 

 bagasse to which w water is added. There is then obtained on crushing 



sugar per unit originally present. Substituting — — for r in the 



expressions already found, the quantity of sugar obtained in the different 

 systems is : — 



Single simple imbibition: — | — = i — 



2 



Double simple imbibition: i — (■ — ; — ) 



^ \z -\- wj 



w-fold simple imbibition : i — { — ; — ) 



\n + wj 



Single compound imbibition 



1 -\- w 



1 -\- w w 



Double compound imbibition : 



w-fold compound imbibition: 



I + w 



w 

 I + w 



\ J. + wj 





1+5^ 



I + W 



- (t - J^' 



\ 1 -\-wJ 



1 -\- w 



Now consider the case where the bagasse contains 50 per cent, fibre (/) 

 and 50 per cent, juice. Let water {w) be added equal to /, 2/, etc. Then 

 in all cases these expressions on computation give the sugar which can be 

 recovered per unit present in the bagasse and independent of the quantity 

 of fibre in the cane ; that is to say, with canes containing 10 per cent, fibre, 

 20 per cent, of added water will recover the same percentage of sugar from 

 that present in the bagasse as 24 per cent, when the canes . contain 12 per 

 cent, of fibre. 



In the graphs in Figs. 143 and 144 are shown values of these expressions 

 for the values of w = f, 2/, etc., i.e., water 10 per cent., 20 per cent., etc., 

 on cane when the fibre is 10 per cent, on cane, and so on. 



The value of the additional sugar obtained wiU be any one of these 

 expressions multiplied by a constant obtained from a knowledge of the 

 selling price of sugar, cost of manipulation, of containers and of freight, etc. 

 The cost of obtaining the sugar will be mainly the cost of evaporating the 

 added water, together with the interest on the prime cost of the additional 

 heating surface necessary. These two items may reasonably be regarded 

 as a lineal function of the added water or briefly by K w, where K is constant. 



