THE CONCENTRATION OF THE SYRUP TO MASSECUITE. 



For s put s -\- d, d being the difference in the solubility of sugar at the 

 two temperatures. 



Then 



1 -f- d dx 



But x has already been shown to be equal to 



I 



m 4- s 

 Making the substitution 



s ds 



d-\- 



*'= ^ + s !!L + J- = 8 ~ dm j (2) 



7 4- /7 ds s -{- m dm 



m -\- s 



As a numerical example let the solubility of sugar be 1*8 and let molasses 

 of 46 purity be required ; the Brix of these molasses will be from equation (1) 



1-8 -h -46 



Now let the solubility of sugar become 2 -5 so that d is -7. The Brix of 

 the molasses then is from equation (2) 



100 x 2-5 - '? X -46 = 82-57 



2-5 -f -46 -7 x '46 



Unfortunately the solubility of sugar in the hot mother liquor (s f in the 

 equation established above) in the pan can not be exactly known ; it is affected 

 by the temperature prevailing, by the presence of non-sugar and by the degree 

 of supersaturation ; now at the temperature 40 C at which it is customary to 

 cure massecuites boiled to grain and cooled in motion the solubility of sugar 

 in water is 2*38 and at the temperature 70 C which is approximately that of 

 the massecuite in the pan the solubility is 3*20 ; the ratio of these is 1-34 ; 

 previously the solubility of sugar in exhausted molasses was taken as 1*8, 

 at a temperature of 27 C ; between 27 C and 40 C the solubility of sugar 

 in water increases in the ratio I'll, and hence at 40 C the solubility of sugar 

 in molasses is taken as Ml X 1'8 = 1-998 and at 70 C 1-998 X l'34 = 2-68; 

 cutting off the decimals then the values of s and s 1 in the equation established 

 above will be taken as 2-0 and 2*7. 



Now owing to supersaturation the lowest solubility possible in the pan at 

 the temperature of 70 C will be 2-7 and it may be considerably higher. 

 Values of the equation 



s 4- m md 



for values of s = 2-0, d= to 1-3 (V = 2-7 to 4-0) and m=3S to 50 

 have been calculated and are given in the table below ; in the vertical column 

 on the left hand side are entered the solubilities of sugar in the molasses in 

 the pan ; in the horizontal caption are entered the values of m from 38 50 . 



365 



