488 Perkins — Rectification Effect in a Vacuum Tube. 



In the following discussion it will be necessary to make 

 some assumption as to the nature of the field produced by the 

 ring-. If it were not for the terminals and galvanometer cir- 

 cuit, we might say that beyond a short distance from the 

 ring the intensity varied inversely as the square of the dis- 

 tance, but the terminals, particular^ when grounded, seriously 

 affect the distribution, and a uniform gradient between ring 

 and terminal probably more nearly represents the actual con- 

 ditions ; at any rate the truth lies somewhere between the two, 

 and we shall make the latter assumption as being the simpler 

 one ; moreover, working out the equation on the other basis 

 does not alter the curves obtained very seriously. A second 

 assumption will be that most of the ionization occurs very 

 near the ring ; this would be the case if the intensity varied 

 inversely as the square of the distance, and unless the gradient 

 is very constant, it w T ill probably be so anyway. When a very 

 long tube was tried the glow was confined to a comparatively 

 narrow region near the ring, and was most intense just under it. 



Let 2m* = the number of ions produced per second by the ring. 

 " T = half period of alternating field. 

 " land d= lengths of two segments of tube as shown in fig. 1. 

 " r = ratio of velocities of ions. 

 " V — effective value of potential of ring. 

 " v = velocity of + ions with unit potential gradient. 



Assume that the 2m ions produced in a second divide between 

 the two segments directly as the gradient of the segments. 



2md 



Then r will travel toward B. 



l + d 



2ml 



And - T will travel toward A. 



l + d 



vV 

 Also —j- will be the velocity of ions moving toward B 



vV 

 And — - " " " " " " A 



d 



during the first, or positive, half cycle ; hence the number of 

 + ions reaching B in this half cycle 



_ 2md I I \ _ 2md I P\ 



- j^d\ ~ w; - j+d y 1 ~vv)' 

 I 



But there will be a certain number of recombinations, during 

 their journey, with negative ions that were repelled during 



*It should be noted that m is a function of V, although no attempt is 

 made at this point to evaluate it. 



