THE SEPARATION OF THE CRYSTALS 417 



are supplied with motors which can develop an excess of power over short 

 intervals. Nevertheless, an individually driven battery is more expensive 

 than one group-driven, and the sum total power of the individual motors 

 will always greatly exceed that of the one larger motor, which need only 

 develop the average power required for a battery, allowing for the time 

 consumed in the five divisions of the cycle. Group drive does not prevent 

 the use of electricity and the centralization of power. The writer inclines 

 to the position that the most generally economical combinations are an 

 electric motor driving a group of machines through the agency of belts or 

 water-driven machines receiving power from a centrifugal pump. 



Load on a Centrifugal. If W be the weight of a particle constrained to 

 move in a circle of radius r and at a velocity v, the centrifugal force exerted 



W v 2 

 is , where g is the acceleration due to gravity. In the case of a machine 



42-in. x 24-in., with steel shell T V m - thick, perforated with T V m - holes 

 at f-in. pitch, the value of W for the shell alone is 180 Ibs., taking the specific 

 gravity of steel as 7 8. The weight of eight hoops of steel each i-in. by J-in. 

 will be 75 Ibs., to which has to be added that of the backing and perforated 

 strainer, amounting to 15 Ibs. ; the total of these is thus 270 Ibs. At 1,000 



Wv 2 

 r.p.m. the value of v is 183 ft. per sec., so that the value of is 146,000 



Ibs. The charge of massecuite will distribute itself in such a manner that 

 its vertical section is a parabola, but with the vertex so distant that it may 

 be considered as a hollow cylinder. The load may be taken as concentrated 

 at the radius of mean position given by the formula 



2 R, z Rj* 



3 -TCI ^2 



where R and R 



are the outside and inside radii of the hollow cylinder. If R 2 be i 75 feet 

 and R l be 1-25 feet, the value of the above expression is very nearly 1-5 

 feet ; for this radius at 1000 r.p.m. v is 157 ft. per sec. If the charge of masse- 

 cuite be 600 Ibs., and if none escape before full speed is reached, the value of 



Wv 2 



- is 308,000 Ibs., so that the total load on the shell of the basket is 454,000 



Ibs. Deducting the area of the perforations the area of the shell is 3,322 

 sq. in., so that the pressure per sq. in. is 136 Ibs. 



The resistant cross-section is that due to the shell and to the rings : 

 for the shell it is ^ X 18 6 X 2 = 7 sq. ins. nearly, after allowing for the 

 perforations. For the rings it is 8 X 2 X I X 0-25, or 4 sq. in., in all a total 

 of ii sq. in. The force tending to break the basket isp d /where p = pressure, 

 d = diameter and / = height. Substituting the calculated values p d I is, 

 136 X 42 X 24, or 137,000 Ibs., so that the stress is 137,000 -r- 11 or 12,400 

 Ibs. (5 J tons) per sq. in. 



Force acting on Molasses. If n be the number of revolutions per sec., 

 r be the radius of gyration in feet, g be the acceleration due to gravity or 



32 feet per sec., the centrifugal force acting on a particle is - - times 



o 



that due to gravity. In the case of a 42-in. machine making 1,000 r.p.m., 



2F 



