132 Capt. E. V. Appleton on the Effects of 



For various arrangements of inductance and capacity 

 consistent with the relation LC = const., the values of 

 frequency as calculated from (3) are practically identical. 

 Thus we may tabulate values of L, 0, and a as follows : — 



L microhenries. 



C microfarads. 



a ohms per henry. 



800 



•00025 



125 Xl0 3 



600 



•00033 



10-83 XlO 3 



400 



•00050 



lOxlO 3 



300 



■000668 



10-4] 5 x10 s 



200 



•00 1 00 



12-5 XlO 3 



100 



•00200 



21-25 XlO 3 



50 



•00400 



40625 XlO 3 



25 



•00800 



80-31 XlO 3 



From these figures it is obvious that there is a minimum 

 value of damping in the neighbourhood of *0005 mfd. 

 Substituting in the formula (5) gives this value exactly as 

 •0005 mfd. 



Thus in a case with no conductance damping (e. g. with a 

 hard tube and applied negative grid potentials) minimum 

 damping is obtained when C is as small as possible, but 

 where grid currents are appreciable maximum control effects 

 are obtained by using capacity values given by equation (5). 



When the conductance is negative (e. g. in a soft tube 

 with applied negative grid potentials) the natural damping 



of the oscillatorv circuit is in 



1 reduced, and for 



capacity values below a certain amount is negative, bringing 

 about the possibility of free electrical oscillations. For zero 



R 



damping we must have k y negative and — numerically equal 



to 



c 



For a definite wave-length X this is obtained when 



67T 



'■£ x 10" 10 farad. 



To 



C is numerically equal to 



illustrate this we may again consider the numerical example, 

 taking k y as — 002 x 10 ~ 3 mho. * In this case for capacities 

 below 3'16 X 10~ 4 mfd. persistent oscillations are obtained 

 in the control oscillatory circuit, the usual retroactive action 

 from the plate circuit being unnecessary. 



The magnitude of the effects of the grid conductance can 

 * E. g. Bown, loc. cit. 



