212 Mr. E. V. Appleton and Dr. B. van der Pol on 



can be applied {e. g. in case of long thin filament) and a fall- 

 in mean filament temperature occurs, which in all proba- 

 bility must be accompanied by a decrease in total emission. 

 A decrease in emission is the only change so far observed 

 by us with ordinary hard receiving triodes. Equation (7) 

 further shows that unless twice the potential difference 

 between the ends of the filament is greater than <f> (4*6 volts) 

 no increase in mean temperature can be expected to occur. 



If we now consider the case in which the anode current 

 varies harmonically between saturation and zero values, as 

 -in an oscillating triode, we see that (7) may be written 



where I a is the value of the saturation current. 



Neglecting the transients we find the maximum amplitude 

 of f given by 



We may now work out a numerical result in the case of a 

 typical 6-volt tungsten filament of diameter 0*01 cm. and 

 length 2' 6 cm. We shall assume the following values : 



a = 5*lxl0" 3 ohm per degree; </> = 4'6 volts ; 



I a = 0"l0 amp. ; p — 2w . 600 ; i fo — 1*0 amp. ; 



4-T' 3 

 2* = 0'4; =^-=l-6xl0- 3 ; 



X 



and 0/= 0*00016 cal. per degree cent. 



On substituting we find that f =-.0'18 degree centigrade, 

 which is practically an inappreciable amount. Taking, how- 

 ever, a frequency of 10 per second, we find ^ = 3*3 degrees 

 centigrade, which change of temperature may bring about a 

 noticeable change in emission. 



The sudden closing of the anode circuit brings about a 

 fall of filament temperature f given by 



f- &~ kE r-f>\ (10) 



/4T 3 \ 



'/° 2R ov¥r+ a ) 



