Perkins — Rectification Effect in a Vacuum Tube. 491 



TOO ( *» "| \ 



N = - „., ' ,^ ^-r 1 {ld\l-d)\ (TrvY-l 2 ) 



In this new factor (TvrV— Z 2 ), we must regard all negative 

 values as zero ; for when f>TwV it shows that no ions can reach 

 B at all, hence no current can flow. Moreover, I is supposed 

 always to be the larger segment, it can thus vary only between 



L and -— , where L is the tube's length. Thus the current 



will begin to flow when TvrV=P, and a plot of the equation 

 between N and I, assuming TVi>V=18 2 and l + d=L='20, in 

 fig. 8 exhibits all the essential features of the experimental 

 curve. Letting TryV = 15 2 gives an even closer similarity, as 

 is shown on the same diagram. The effect of assuming a 



distribution unaffected by the ends ( i. e.,— -J is to make the 



slopes more abrupt than those shown. 



One more possible effect ought to be considered ; the possi- 

 bility of a variation in the total ionization for different posi- 

 tions of the ring. For instance, the number produced on 

 either side of the ring might depend on the gradient on that 

 side. Let ft = the number of ions produced per second, per 



n V 

 unit gradient. Then —j- will be produced on the side toward 



n V 



B and — — on the side toward A (assuming as before that 

 a 



nearly all the ionization occurs very near the ring). Then 



total ionization = n T , — - =2m. Substituting this in the last 

 Id & 



equation, we have 



N = J^^l » W-d) (TrvV-P)} 

 Vv*(l + d)r m ' v ; ; 



which yields the curve shown in fig. 9, which does not differ 

 very materially from that in fig. 8. 



The variation of potential as exhibited by the electro- 

 static voltmeter is easily explained by considering the 

 potentials, due to the ring, at A and B. When the galva- 

 nometer circuit is to open the ends will not affect the field 



so much, and we may assume P a — — and P b = — when 



CI I 



Q is the charge on the ring. Then P a — P h = P.D. = Q . 



This gives a curve very similar to the one obtained, although 



