﻿Electric Waves obtained by Valves. 173 



and similarly for (2). Hence, if all the electrons returned 

 to the grid an oscillation would not be maintained. The 

 possibility of a maintained oscillation depends in this case 

 on the fact that in each oscillation a certain group of the 

 electrons are collected on the plate and the integral of (2) 

 does not in consequence include all the values of t between 



2-7T 



and - and its value is not therefore zero, but may be 



P 



negative. 



The first step is, therefore, to find which electrons reach 

 the plate. When there are no oscillations the electrons have 

 sufficient energy on passing the grid to just take them to the 

 plate against the potential V, and if therefore any extra 

 work is done on them they will be collected on the plate, 

 but if the work is negative they will fall shore of the plate 

 and return to the grid. Expression (1) shows that all the 

 electrons which pass through the grid at times t , such that 



Tcos/>^ sin pt — sinp(T + '. . . .,, , , 



; + — —- 1 — is positive, will reach the 



• P l r 



plate, while chose for which it is negative just fail to reach 



the plate and return to the grid. 



Of the electrons then which pass the grid half go on to 

 the plate and half return to the grid, the electrons running 

 to the plate for a time equal to ir\p (half the periodic time 

 of the oscillation) and then running back to the grid for 

 time 7r/p and. so on. But the total work done by the 

 oscillating potential on the two halves as they go from 

 grid to plate is zero : and therefore the net work done 

 is the work done on the return journey on the half which 

 returns to the grid. 



To find therefore if an oscillation whose periodic time is 

 2irlp and amplitude V can be sustained by a grid voltage V 

 it is necessary first to find the time T which the electrons 

 take to pass Irom the grid to the plate under the field due 

 to V alone, next to find from equation (1) the values of t Q 

 for those electrons which return to the grid when the 

 system is oscillating, and, finally, by taking the mean value 

 of expression (2) for these values of t and, knowing the 

 emission current, to find the total work done per second by 

 the oscillating potential. If this work is negative and at 

 least equal to the dissipation loss per second, the oscillation 

 will be maintained. 



A table of calculated approximate results is given below 

 for various values of the ratio T : l/p. The second column 

 gives the values of pt for the electrons which return 



