47 6 Mr. E. Talbot Paris on the Polarization of 



From this, if r x and r 2 are the distances from the axis of 

 the centrifuge to the surface of the liquid in the tube, and to 

 the bottom of the tube, respectively, when the centrifuge is 

 working, then a { and a 2 corresponding to the times r x and t 2 

 can be determined. 



In general the average radius of the particles in the re- 

 sulting suspension will not be the arithmetic mean of a x and 

 « 2 , and may not even be between them. 



Suppose that initially the suspension contains an equal 

 number of particles of all sizes within reasonable limits — 

 say N particles of each kind per cubic centimetre. In 

 practice it is immaterial whether or not the condition is 

 strictly fulfilled provided it obtains in the neighbourhood of 

 those particles which it is desired to separate into a uniform 

 suspension. Let this suspension be centrifuged for a time t. 

 Then, if the centrifuge works perfectly, all particles having 



radii greater than 



, / 9v r 2 \i 



will be removed. 



To find the number of particles removed having radii 

 equal to a, less than a', we must find r, the distance from 

 the axis from which the last particle of radius a to reach the 

 bottom of the tube, at r 2 , started. 



If 



p= 2a) 2 (p-p') 



then 



r 9 



and r = log e { log f r 2 — C . a 2 r} . 



The number removed is (r 2 — r)N, supposing the tube to have 

 unit cross-sectional area ; while the number originally present 

 is (r 2 — •? , 1 )N. The proportion removed is therefore 



r 9 — r 



\og e - l {\og e r 2 — C.a 2 r} 



r 2 — r x 



and the proportion remaining is (1—p). 



Some calculations have been made, based on the dimen- 

 sions and speed of the centrifuge used in the present ex- 

 periments. The results are shown in fig. 4, where the 

 percentage of particles is plotted against their diameter. 



