58 BELL SYSTEM TECHNICAL JOURNAL 



upon the assumed direction of /. In some instances all solutions may 

 correspond to physically realizable distributions for the double in- 

 jection case. The solutions will, in general, require that the potential 

 zero be located at different places and may require that the net flow 

 of current across the zero plane be in opposite directions. The 

 physical reality of each of these distributions must be checked by 

 noting the value of Z for the indicated solution and solving for the 

 derived current (2 — Z)I on the injected side of the zero potential 

 plane and the derived transmitted current ZI. If these are respec- 

 tively greater than the numerical values of la and /& (paired consistent 

 with the assumed direction of injection) the indicated solution is 

 possible. In addition there may exist a solution in which the currents 

 la and lb are each totally reflected at two different zero potential 

 planes, separated by a region of zero potential. The possible existence 

 of this solution must be tested for separately. 



Electron Transit Time 



So far no use has been made of the dashed curves shown in Figs. 2, 

 3 and 4. These give the electron transit time from the first plane 

 to any desired plane. The significance of the unit of time is to be 

 found by again referring to Fig. I. The time an electron takes to 

 travel from the cathode to the first plane is given by 



/o = c ^ = 7.72 X 10-" -^ (seconds). (10) 



This value of /o is a natural unit of time to be used whenever the condi- 

 tions at the first plane are expressed by Vi and / just as Sq is a natural 

 unit of distance. Accordingly, electron transit times from this plane 

 to any other plane are expressed in units of /o- The time in seconds is 

 then 



T = Tt,. (11) 



Transit times for reflected electrons are not given but may be com- 

 puted by taking the time to the reflection plane and adding to it the 

 returning time. This latter is obtained by taking the difference be- 

 tween the time to the reflection plane and the direct time to the plane 

 under consideration. 



Circuit Characteristics 



In many practical cases the first plane will coincide with a mesh or 

 grid electrode in a vacuum tube and the second plane will correspond 

 with a plate electrode. Under these conditions the current-voltage 



