CANE SUGAR. 



of the whole mass in the pan. Suppose it has been found by experience that 

 a mass of 50 apparent purity gives the best results when boiled to an 

 apparent Brix, as indicated by the brasmoscope, of 90 ; when this factor has 

 once been determined it is an easy matter to boil all subsequent strikes of this 

 purity to the same elevation of the boiling point, and this can be done more 

 exactly with the aid of graduated instruments than by the sense of touch of 

 the most experienced sugar maker ; the illustration given above demands, 

 of course, that the nature of the non-sugar does not vary. 



From the formula or table it follows that a massecuite of 50 purity con- 

 centrated to 80-86 Brix will give molasses of the same purity as one of 55 

 when concentrated to 82-44 Brix. The ratio between these two Brix is 

 82-44 -f- 80-66 = 1-0195. Hence the required Brix as indicated by the bras- 

 moscope is 86-5 X 1-0195 = 88-19, i.e., if a massecuite of 50 purity gives 

 molasses of 46 purity when concentrated to 86*5 Brix as indicated by the 

 brasmoscope, a massecuite of 55 purity will give molasses of the same purity 

 when concentrated to 88-19 as indicated by the brasmoscope, 



The application of the brasmoscope readings to control the water content 

 of massecuites boiled to grain is complicated in that the instrument does not 

 give the Brix of the massecuite as a whole but of that of the mother liquor ; 

 what is required to be known may be expressed thus : What shall be the 

 Brix of the mother liquor in the pan at the moment of observation so that 

 on cooling exhausted molasses result ? And algebraically the problem can be 

 solved thus : 



Let the solubility of sugar in molasses at a low temperature be s and let it 

 be s' at a more elevated temperature ; it is required to find what must be the 

 Brix when the solubility is s' so that the purity is m when the solubility is s. 

 Let x be the Brix of the molasses when the solubility of sugars is s. 



Then 



1 x =. water 



* (1 x) =. sugar 

 and 



s (1 x) 



m =. 1 



x 



whence 



*=7^ C 1 ) 



Now let the solubility of sugar change to s 1 , all other factors remaining the 

 same. 



The absolute amount of sugar in solution now is s 1 (1 x}, the water 

 and non-sugar remaining the same. 



If the Brix be now denoted by x 1 , 



364 



