468 Mr. J. J. Lonsdale on the Ionization 



near the centre at the electrode was never greater than 

 3500 volts per cm. 



The curve giving the relation between the current on the 

 central electrode and the voltage on the outer tube when 

 ions of varying mobilities are present : — 



The velocities of the ions under a gradient 



of a volt-cm. are respectively .... u l9 it 2 , u 3 , . . 



The number of ions per c.c. of each kind . n v ?i 3 , n 3 , . . 

 Saturation voltage of each ion (ascending 



order) V lt V a , V 3 ,.. 



The time for the air to pass the electrode . t sees. 



The measure of the blast B c.c. per. sec. 



Let r be the greatest distance from which an ion can be 

 driven into the electrode by a voltage V, then 



o , 2Ytu 



i b ' 



° a 



Then in one second the ions will be driven into the electrode 

 from the volume 



B(r 2 -a 2 ) 

 (I> 2 -a 2 ) ' 



If e is the charge on an ion, then the current due to a 

 particular ion is 



en(r 2 — a 2 )B 

 {b 2 -a 2 ) ' 



The whole current due to any voltage V, when that voltage 

 is less than Vi the saturation voltage of the fastest ion, is 



-^^^{{r 2 -a 2 )n 1 ^(r 2 -a 2 )r i2 +(r 2 -a 2 )n z + }, 



j ( Vw^! + Yu 2 n 2 + Yu»n d + ), 



(b 2 -a 2 )\og e - a 



or C = kiYu-^n-^ -f Yu 2 n 2 + Yu 3 n 3 4- ), 



where h is constant, and as u and n are also constants this 

 part of the curve is a straight line through the origin. If 

 the voltage lies between Y x and Y 2 then the current 



= hiYiU-i^ + Yu 2 n 2 -f Vw 3 n 3 + ) . 



