242 CHAPTER XI 



Let the juice in the bagasse contain s sugar, of which p is recovered in 

 the subsequent operations. Let the value of the sugar, after deducting all 

 charges for containers, freight, overhead, etc., be v, and let the efficiency 

 of the added water be e. For convenience of writing denote any one of the 

 above expressions by / (w). Then the value of the sugar obtained is 

 s p v e f (w). 



The variable expense to be charged against the value of the sugar is the 

 cost of evaporating the water, together with the interest on the prime cost 

 of the larger heating surface required. Both of these may be regarded as 

 a lineal function of w, so that the cost may be expressed as Kw where K 

 is constant. 



Now the extreme values of s may be taken as 10 per cent, and 16 per cent., 

 of p as 70 per cent, to 85 per cent., of v as $30 to $60 per ton, and e, about 

 which the literature of the cane affords little information, will be taken as 

 50 per cent. 



The lowest value of s p v e will then be o 10 X 0-70 X 30 x 0-50 = 

 $1*05, and its highest value will be o 16 X 0-85 X 60 X 0-50 $4-08. 



With quadruple effect evaporation it is permissible to accept an evapor- 

 tion of 30 Ibs. water per Ib. of coal. If the coal costs $10 per ton, the cost 

 of evaporating a ton of water will be 30 cents. On the other hand, some 

 plantations are very favourably situated with regard to local supplies of 

 cheap wood, and are able to evaporate water at a much cheaper rate. The 

 cost of evaporating a ton of water will then be taken as lying between the 

 limits of 10 cents and 30 cents. 



In the case of single imbibition, simple or compound, with the lowest 

 values of s, p and v, and with coal at $10 per ton, as representing unfavour- 

 able conditions, the economic extraction curve expressed in cents per ton 



of cane will be found by plotting values of I 05 X -j- o 310, the maximum 



point being determined as already indicated. 



In Figs. 145 and 146 are given twenty-four such graphs. They are 

 calculated for/ (w) 0-3 w, 2 / (w) 0-2 w and 4 / (w) o-i w, f (w) 

 denoting any one of the expressions representing the effect of the added 

 water. The values selected are intended to represent unfavourable, average 

 and favourable conditions, and are numbered i, 2, and 3 in this order. 

 In calculating the numerical values to obtain points on the curve the canes 

 have been accepted as having 10 per cent, of fibre and the bagasse as con- 

 taining 50 per cent. As abscissas are laid out values w = i, 2, 3, etc., the 

 corresponding values of n f (w) being plotted as ordinates, and representing 

 the profits as cents per ton of cane. 



Referring to the graphs in Figs. 143 and 144, the superior action of 

 compound imbibition is very clearly shown, especially in the longer trains, 

 where the curve rises very sharply from the origin. Similarly it will be 

 seen that the subdivision of the water used in schemes of simple imbibition 

 is not attended with any very great benefit, double compound imbibition, 

 for example, showing better results than does the quadruple simple process. 



Inspection of the economic curves shows that generally they rise steeply 

 from the origin, and that they do not present a " peaked " but a " flat " 

 maximum, that is to say, there is a region over which the profits due to 

 imbibition are sensibly constant, and it should be over this region that 

 the factory is operated. It is also worth while noticing that with the 

 compound schemes the economic maximum is reached with a less quantity 



