﻿Electric Waves obtained by Valves. 171 



With these assumptions we shall only attempt to show that 

 an oscillation can be maintained of about the right order of 

 wave-length. 



The principle involved is the following : — 



Suppose the filament and plate are at zero potential and 

 the grid at + V ; then the electrons from the filament which 

 pass through the grid with a velocity v due to the potential 

 V come to rest at the surface of the plate and return to the 

 grid, which they again reach with velocity v. In the space 

 between the grid and the plate the total work done by the 

 fixed potential V on the electrons which move in this space 

 is zero, all the work having been done between the filament 

 and grid. 



If now superposed on the fixed potentials there is an 

 alternating potential V s'mpt between grid and plate due to 

 oscillations, the work done by the potential V sinp£ on the 

 electrons is not necessarily zero. If the work is positive the 

 electrons are abstracting energy from the oscillating system, 

 and the average velocity with which the electrons hit the 

 grid is increased ; the oscillations cannot in this case be 

 sustained by the movement of the electrons. But if the work 

 is negative the electrons are giving energy to the oscillating 

 system, and if the rate at which this energy is given is at 

 least equal to the rate of dissipation of energy in the oscil- 

 latory circuit by resistance, radiation, or dielectric loss, the 

 valve will maintain the oscillations. The average velocity 

 with which the electrons hit the grid is in this case less than 

 the velocity r due to the potential V which they acquire 

 between fliament and grid, and hence the energy put into the 

 system from the battery Y is not all used in heating the grid 

 but part is turned into energy of oscillations. 



The above argument is not affected if, in consequence of 

 the oscillation, some of the electrons are collected on the 

 plate. In all cases, provided the total work dune per oscilla- 

 tion by the alternating field is negative, an oscillation can 

 be sustained if the dissipation of energy in the oscillatory 

 circuit is not large. 



8. The particular case in which the filament and the plate 

 are at the same potential when there are no oscillations may 

 be considered first. Let V be the potential above the plate 

 of the grid and cl the distance between them. 



"When there are no oscillations the electron passes the grid 



with velocity v\ = \/ — V and is then subject to a constant 

 retardation/, which brings it to rest just at the plate. If T 



