the Form of Free Triode Vibrations. 



209 



■second for zero collected emission we have, with the assump- 

 tion that the resistance of the filament is not materially 

 altered, W' = //R, and thns the increase of energy supplied 

 to the filament when the anode circuit is closed is 



W-W'=(O'4E-0)i o , 



(1) 



where E is the filament voltage. 



But for small triodes E is never greater than 6 volts, 

 in which case the quantity W — W v is negative since <f> 

 for tungsten is 4*6 volts; that is, the filament as a whole 

 is cooled, resulting in a reduced emission. As the above 

 treatment is very approximate indeed, it is hardly to be 

 expected that the result (1) is strictly accurate but, as will 

 be shown later, the cooling effect suggested is actually met 

 with in practice. 



It now remains for us to consider the effect of these 

 temperature variations for a filament of ordinary size when 

 the anode current is periodic. 



EZS 



Fig. 7. 



— Mi| B - --Mil 



22ZZM 



P*i 



Consider a small element dx of filament, when no ther- 

 mionic current is allowed to flow. Let the temperature of 

 this element be T , and its resistance r dx. With the as- 

 sumption that all energy supplied is lost as electromagnetic 

 waves, we have for the steady state 



*/* r o 



dx=sT n Kda 



(2) 



where if is the filament current and s the Stefan-Boltzmann 

 constant (relating to unit length of filament). 



When the anode circuit is closed, the emission current 

 will divide itself between the two branches of the filament 

 circuit. Let the Hh part of the total anode current /„ run 



