THE lONlSAtlON OF Till-: AJK. 269 



from the other. The following consideration shows this 

 clearly : — 



The equation to the path of an ion at a distance r from the 

 common axis of two concentric cylinders of the Ebert or Gerdien 

 type is : 



Where U is the velocity of the air stream parallel to the axis of 



dr YLv 

 ~dx """T7 



the cylinders, i.e., the x axis ; 



and E is the electric intensity at a point distant r from the axis, 



and acting at right angles to the axis. 



If Q is the charge on the inner electrode, and / is the length 

 of this electrode, 



A -rr Q 



E = 



2 TT I- I 



Hence -. — <^-i' = 2 tt r C dr. 



If a is the radius of the innter electrode, and h is the inside 

 radius of the outer cylinder, an ion initially at a distance r=h 

 from the axis will be caught by the inner electrode after travelling 

 a distance x parallel to the axis, where x is given by 



X = / 2 TT /- dr. 



TT 0- — TT a-J 



1 .V 



where N is written for the quantity of air drawn from between 

 the cylinders per second. 



Hence all ions of mobility v which enter the space between 

 the outer and inner cylinders will be caught by the central elec- 

 trode, provided / is made just greater than x; 



I N 



i.e., I > 



4 TTV Q 



C V 1 



or -— -— > 



A^ 4 TT V 



where C is the capacity of the innter and outer cylinders, and 

 V the potential to which the inner is charged. 



Hence, if an inner electrode is to collect all small ions — that 

 is, ions of average mobility, i . 5 cms. per sec. per volt per cm. — 

 the condition to be satisfied is : 



