ULTRA-HIGH-FREQUENCY VACUUM TUBES 651 



tion applicable to them that the planes A and B in Fig. 1 are very 

 near together compared with x^ and Xp. As a first consequence of 

 this assumption, the electron velocities at B must be the same as those 

 at -4, and hence one of the initial conditions at the J5-plane is provided 

 for. A second consequence is that the potential at B is the same as 

 that at A, and therefore the potential between plate and cathode is 

 the sum of the potentials between cathode and A and between B 

 and the plate. 



The accelerations at the two planes are not the same. This can be 

 seen from the lower diagram in Fig. 1 when it is remembered that the 

 acceleration is proportional to the slope of the potential curve. The 

 accelerations can be found, however, by a relatively simple calculation 

 and this will be done in the course of the following analysis. 



D.-C. Relations 



As a preliminary to the treatment of first order effects in negative 

 grid triodes, certain d.-c. relations will be determined. 



The distance is related to the transit time by (10). At the cathode 

 and for complete space charge the acceleration and velocity are zero, 

 so that the cathode-grid transit time Tc is given by 



Xc = K^' (54) 



At B the acceleration is yet to be found, but may be taken to be g 

 times that at A. Hence, from (21) 



aB = gKTc. (55) 



The velocity at B is the same as that at yl, so that from (27) 



ub^K^' (56) 



These values, (55) and (56), may now be inserted as initial conditions 

 in (10) to give a relation between Xp and Tp. Calling the ratio TpjTc 

 by the symbol h and XpjXc by the symbol y we thus obtain : 



^/j2 = yjz - h - h'l3. (57) 



In this way the acceleration is related to the transit times. These 

 have now to be expressed in terms of quantities that can be measured 

 directly, namely the current and the plate voltage. To do this, the 

 general expression for potential difference is obtained by integration 



