Grid Currents in Three-Electrode Ionic Tubes. 131 

 and is given by 



E=A,-^-s)' C0S (^_(B_^y t ) r . (2) 



which represents a damped oscillation of frequency n 

 given by 



1 / 1 / R " «j \ 2 

 n ^27rV LC"(2L"20)' 



(3) 



and where the damping factor a is given by 



«=l(? + K o) W 



These equations show that the damping factor of a free 

 oscillation is altered by the presence of the conductance, 

 being increased or decreased according as the conductance 

 is positive or negative. 



Let ns consider the case where the conductance is positive. 

 For any given frequency there is a particular division of 

 inductance and capacity which produces a minimum damping 

 factor. This can obviously be obtained by finding when cc in 



(4) is a minimum. Now, let TTT = a) 2 , where (o = 2irn and is 



therefore approximately constant. After substituting for L, 

 the value of capacity which gives minimum damping is 





found to be 



Thus for a wave-length of X cm. the particular value of 

 capacity producing minimum damping, and therefore 

 maximum electrostatic effect on the grid, is given by 



C=^\/§xlO- 10 farad (5) 



This result is best illustrated by the consideration of a 

 typical case where the conductance is positive for the 

 particular operating point considered. 



Suppose R=4 ohms, 



L=10~ 4 henry, 



C = 2xl0" 9 farad, 



*«! = 5x 10" 6 mho. 



* See Bown, Phys. Rev. 10, pp. 253-265. 

 K2 



