648 BELL SYSTEM TECHNICAL JOURNAL 



worked out so that Maxwell's analysis is our only basis at the present 

 time for determining how near to the grid we can imagine A and B to 

 be fixed. 



The distance from cathode to grid will be called Xc and from grid to 

 plate will be called Xp. Corresponding to Xc there will be an electron 

 transit time Tc, and to Xp there will be the transit time Tp. The 

 density of the total current leaving the cathode is Ic so that the current 

 factor el/kme will be Jc. The factor for the density of the total 

 current reaching the plate will be Jp. 



The general scheme for analysis of the triode is to regard the struc- 

 ture as composed of two parallel plane diodes. The first of these 

 comprises the cathode and the imaginary plane A, while the second 

 comprises the imaginary plane B and the plate or anode. In accord 

 with normal operation, complete space charge is postulated at the 

 cathode, so that initial velocities and accelerations are zero, and the 

 general parallel plane equations, (41), (42) and (43) may be applied 

 directly to conditions between the cathode and the plane A. 



The plane B and the plate also constitute a structure to which the 

 general equations can be applied, but first the initial velocities and 

 accelerations at B will have to be found, and finally a relation between 

 Jc and Jp will be needed. Moreover, the relation of the potentials at 

 A and B to the potential Vg of the grid wires themselves must be 

 found, because it is only the latter that is available for external use or 

 measurement. 



As an aid to finding these various relations the lower diagram in Fig. 1 

 will be of assistance. This is a graph showing the general form of the 

 d.-c. potential as a function of the distance from the cathode. Between 

 cathode and plane A the potential curve is the same regardless of 

 whether the line 1-2 in the upper diagram which passes between two 

 grid wires is followed, or whether the line 3-4 which passes through a 

 grid wire is followed. The same thing applies between plane B and the 

 plate. 



Between planes^ and B, however, conditions become vastly different 

 according to whether the potential curve is drawn for the line 1-2 or the 

 line 3-4, and the general shape of the potential curve for the two 

 conditions is marked 1-2 and 3-4 respectively in the lower diagram. 

 Along 1-2 the potential is everywhere positive, as otherwise electrons 

 would not be able to penetrate the grid mesh and reach the plate. On 

 the other hand, the grid wires themselves are at a negative potential, 

 and the curve 3-4 shows the way in which the potential surface forms 

 into pockets surrounding the grid wires. The size of these pockets, 

 and hence the location of the planes A and B is determined by the 



