558 CHAPTER XXVII 



finally purified material whence sugar is removed as crystals. As long as 

 the principle of the formula is understood, the basis of reference is a matter 

 of indifference. 



The general control formula discussed in detail above may be used as a 

 starting point to deduce other formulae of use in control. These, which 

 follow from simple algebraic transpositions, are collected below, and from 

 them passage by means of constant multipliers may be made to commercial 

 standards of reference, such as " gallons of molasses per bag." 



Let s denote the purity of the final product : raw sugar, or refined sugar, 

 in which case s = I. 



Let j denote the purity of the initial material : syrup in a raw sugar 

 house and raw sugar in a refinery. 



Let m denote the purity of the by-product : molasses in a raw sugar 

 house and " barrel syrup " in a refinery. 



Then :- 



1. s (j m) /j (s m) = sucrose in product per I sucrose in initial 

 material. 



2. (j m) Ij (i m) = product = sucrose in product = solids in 

 product per i sucrose in initial material, when referred to refined sugar 

 as product. 



3. m (s j) I j (s m) = sucrose in by-product per i sucrose in initial 

 material. 



4. m (I j) jj (i m) = sucrose in by-product per I sucrose in initial 

 material, when referred to refined sugar as product. 



5. j m/s m = solids in product per i solids in initial material. 



6. j m/i m = product = solids in product per i solids in initial 

 material, when referred to refined sugar as product. 



7. s j /s m = solids in by-product per i solids in initial material. 



8. i j /i m = solids in by-product per i solids in initial material, 

 when referred to refined sugar as product. 



9. s j jj m = solids in by-product per i solids in product. 



10. i j jj m = solids in by-product per i sucrose in product, per 

 i solids in product, per i product, when referred to refined sugar as product. 



11. m (s j) /s (j m) = sucrose in by- product per i sucrose in product. 



12. m (i j) jj m = sucrose in by-product per i sucrose in product, 

 per i solids in product, per i product when referred to refined sugar as 

 product. 



Again, Up sucrose in initial material, especially raw sugar, then 

 I 3- P (J m ) IJ ( T m) = sucrose in product = solids in product = 

 product per i of initial material, referred to refined sugar as sole product. 



14. Non-sugar in raw sugar /non-sugar in barrel syrup = barrel syrup 

 per I raw sugar, where refined sugar is the sole product. 



15. If s x and s 2 be purities of the product, then 



sucrose in raw sugar of s, purity s t (s 9 m) s z m . 



^~? = 1 ; 2 _ ( = _ where Si = i, 



sucrose in raw sugar of s 2 purity s 2 [Sj m) s 2 (i m) 



i.e., with reference to pure sugar. 



These formulae may be used to solve many problems, some examples 

 being appended. 



i. What are the comparative weights of raw sugar of composition 

 (a) 96 o per cent, sucrose, 96 3 gravity purity, and (b) 97 o per cent, sucrose, 



