THE EXTRACTION OF JUICE BY MILLS. 



Consider the movement of a pointy (Fij. 115} using a system of polar 

 co-ordinates the point p will reach A in time t with a velocity V\ this 

 velocity can be divided into two components c and w, of which c is in the 

 direction of the radius vector and w is perpendicular to it. The crushed cane 

 must move over the trash turner in such a way that these components are 

 constant, a result to be obtained by the following conditions : 



FIG. 114. 



If r and u are the polar co-ordinates of the point p, then 



dr 

 C = -j7 or dr = c dt, 



now, since C i3 constant, one obtains by integration 



r ct + <?!. 



The value of C l is obtained by considering that when t o, r must be equal 

 to R. Using these equalities it follows that 



Further 



C l = R 

 r = ct + R 



r .du 



w = 



(1) 



dt 

 or w.dt = r.du. 



The value of r can be obtained by substitution from (I) whence it follows that 



w.dt (ct + R) du 

 or w . dt 



ct + R 



= du. 



On integration 



w 



u = - log (R + ct) -f C 2 . 



The constant C 2 can be obtained by putting t o and u = o, whence 



C, = - log R. 

 185 



