440 CHAPTER XXI 



the quantity of refined sugar that can be obtained from a juice is constant 

 and independent of the number of operations and also independent of the 

 purity of a raw sugar obtained as an intermediate product : — If raw sugar 



is made of purity s the quantity of sucrose contained therein is ^-p^ {. 



J (s — m) 



If this raw sugar is refined, per unit of sucrose present there is obtained 



s~m . . , . . . . .. . sij — m) s—m 



and per unit oi sucrose m the origmal juice ^ ~ x — 



s(i— m) j{s—m)s{i—m) 



j — ni 



-T—. ^. and the same result will follow when s chane^es to s, or any 



J {i —m) b 1 J 



other value. This is also the same quantity of sugar that will be obtained 

 if pure sugar is made directly from the juice. The argument given above 

 assumes that the molasses obtained by the producer and the refiner are of 

 the same purity. 



The Value of the Crop to the Producer and the Conditions of Sale. — Since 

 for every percentage of sucrose and for every purity there is produced a 

 different weight of raw sugar, the money received by the producer will vary 

 for every case. This variation is also controlled by the conditions of sale. 

 The basis of sale at present obtaining in the United States markets is : — 

 The price quoted refers to sugar of 96° polarization ; for each 1° above this 

 standard the sugar receives a bonus of 1/32 cent per lb. and for each i" 

 below a fine of 1/16 cent per lb. is imposed. The fine and bonus are in- 

 dependent of the market price, whether 2 cts., 3 cts., 4 cts., etc., whereas 

 it is evident that both fine and bonus should be in proportion to the price. 

 Hence a fine or bonus just at one price must necessarily be unfair at another. 

 These figures also only refer to the limits of 94° and 98° polarization, sugars 

 above the latter figure receiving no extra bonus and sugars below the former 

 being only sold on special terms. The basis of sale is also faulty in that it 

 does not take into consideration the purity of the product on which, equally 

 with the polarization or percentage of sugar, the yield is controlled. 



Taking as a first approximation that the value of the sugar is proportional 

 to the polarization, it is easy to see that 1/32 cent or 0-03125 cent per lb. 

 per 1° fairly well represents the increased value when sugar is at 3 cents, 

 and that at 2 cents the producer is benefited, the buyer losing with sugar at 

 4 cents. Similarly, a mental calculation will show that the buyer gains in 

 all cases when sugar is fined 1/16 cent or 0-0625 cent per 1° below 96 test. 

 The question is, however, more complicated than this and may be treated 

 thus : — In the previous section it was shown that the relative quantity of 



J J • ■ 1- .!_ ■ s ii —m) 100 . ^ . 



raw sugar produced is given by the expression — ^^ ~ x -7- where p is 



the percentage of sucrose in the raw sugar. With sugar quoted at c cents 

 per pound the sugar will sell for 



{s (i — ni) 100 1 { , ij. r^ I . r 



-! — ^ X — — \-X \c -\- ip — 96 X 0-03125 r cents, or for 



\ s — m P \ \ J J f 



{s (i — m) 100) ( , r ^s r ^ . 



I I _^ X — Ix j^- (96 -;^) X 0-0625' cents. 



The net income rece':ved by the producer will be this quantity less the ex- 



