556 CHAPTER XXVII 



per cent, cane would be less than dilution per cent, normal juice. Only 

 part of the added water appears, however, in the mixed juice, and unless the 

 admixture is very low the figure for dilution per cent, normal juice will be 

 less than added water per cent. cane. 



The Control of the Boiling House.* — ^The proportion of sucrose which can 

 be obtained from that present in the juice depends on the purities of the 

 original material, of the raw sugar, and of the waste product or molasses. 



From the comparison of the amount actually obtained with that calcu- 

 lated from the observed purities, a control over the operations in the 

 boiling-house follows. The fundamental formula msiy be obtained thus: 

 From a material containing j sugar per unit weight of dry substance let 

 there be removed c sugar and d non-sugar and let (c + d) contain s sugar per 

 unit weight of dry substance. The residue (molasses) is {i — c — d) and 

 let it contain m sugar per unit weight of dry substance. Then _;"= (c -f-^) 

 s + (i — c — d) m. This equation can be transposed to the form c -\- d = 



. Multiplying both sides by -^ the following equality results : — 



s [c -\- d) __ s {j — m) 

 j ~ j (s —7n)' 



Now, s {c -{- d) is the sucrose in the product (raw sugar) and j is the 



5 ic -\- d) 

 sucrose in the original material, so that the expression — ^^-^ is the 



sucrose obtained in the raw sugar per unit of sucrose in the original 

 material. This quantity is termed the available sucrose, so that 



c / -y Tft) 



available sucrose per cent. = -r^- r X lOO 



^ J [s — m) 



where s, j and m are the purities of the raw sugar, the original material, 



and the molasses. 



If sucrose or pure sugar is the product made, then s becomes unity 



and the formula reduces to ~ , . 



J {I — m) 



This formula has been dedured above as applied to sucrose and dry 

 substance, that is to say with regard to absolute purities. In its deduction 

 the only postulate required is that the following self-evddent relation 

 holds : — 



Dry substance in juice = dry substance in raw sugar -f dry substance 

 in molasses. 



Evidently for dry substance may be substituted gravity solids provided 

 a similar relation holds in this case, and this relation does hold when the 

 gravity solids of the original material, of the raw sugar and the molasses 

 are determined in eqital concentrations of non-sugar. 



c { 1^ yfi\ 



The value of the expression loo X r-)^ [ is used by the writer as the 



'■ J [s ~ m) 



available sugar, and it gives the quantity of sucrose in raw sugar of purity s, 



• Formula for available sugar have been chiefly developed in Java by Winter, Geerligs, Rose, Carp, Lobman and 



40 

 Hazewinkel. The form usually employed is that due to Winter : Available sugar = S X 1.4 X -p- where S and P 



are the polarization and the polarization gravity purity of the raw juice, and the available sugar is expressed as 

 96 test and not as sucrose. Algebraically this form is the same as that developed by the writer, who, however, 

 was anticipated in its use by HuUa in the beet sugar industry. A very complete discussion of the work done on 

 control formulas in Java will be found in the Dutch Editions of Geerligs' " Cane Sugar and its Manufacture." The 

 writer has preferred to present the matter here as he himself has developed it. 



