THE SEPARATION OF THE CRYSTALS 421 



interstitial space is md where m is constant and the number of spaces in 

 unit area ^ where m is constant. The flow of a fluid through a capillary 



tube is given by Poiseuille's law, which states that the rate of flow is propor- 

 tional to the fourth power of the diameter of the tube. It hence follows 



k d* 



that F ==- = kd 2 where k is constant, or the rate of flow of the molasses 

 a* 



in a centrifugal will vary as the square of the diameter of a crystal. 



Again, if there be n crystals in unit volume of massecuite, the diameter 



of each crystal will be 5 -== where c is constant ; it follows then F = ^ 7=. 

 Vn V 



where c is constant ; also for n may be put v where v is the quantity of 

 syrup from which grain is formed or pied-de-cuite left in the pan, whence 



k 

 also F = = where k is constant. 



Vv" 



The initial basis of reasoning adopted in this section assumed that all 

 the circles were of equal size ; if there are introduced smaller circles, as in 

 Fig. 266, these may be inserted between the larger circles, thus closing up 

 the interstitial spaces forming the capillary tubes. This is precisely what 

 happens when the operator obtains an uneven grain or when a second 

 granulation known to operators as false grain occurs. It is then easy to 

 realize that evenness of grain is of much more importance than is diameter 

 of crystal. 



The other conditions governing the quantity of water that remains in 

 sugars may be discussed here. This quantity will be controlled firstly by 

 the pressure acting on the molasses, which is a function of the centrifugal 

 force in turn controlled by the speed of rotation. A second factor is the 

 viscosity of the molasses, and, though no definite relation can be stated, the 

 greater the viscosity the greater will be the quantity of molasses adhering 

 to the crystal. This effect can be controlled by drying the massecuites 

 hot as they leave the pan, or by diluting the film of molasses as by washing 

 with water in the machine. 



A third factor is the surface area of the crystal to which the quantity 

 of molasses adhering is proportional. The surface area is inversely pro- 

 portional to the diameter of the crystal, so that, if w is the water remaining 



k 

 in the sugar, w =-^ where k is a constant and d is the diameter of the crystal. 



The only experiments dealing with the discussion above that the writer 

 has encountered are due to Geerligs. 2 He made mixtures of 600 grams of 

 crystals of varying diameter and 400 grams of syrup, after which the magma 

 was allowed to drain for three days, affording the results tabulated below. 



Diameter of Grain, Syrup run off P 



m.m. = d. grams = F. ~ffi 



3-o 30 33 



2-0 . . 265 . . 66 



i -5 . . 200 . . 89 



I -o .. 115 .. 115 



0'5 . . 20 . . 80 



