460 'Temperature of Cathode and Anode in a Geissler Tube. 



These relations are true whether the cathode glow is 

 normal or abnormal ; for the linear relationship between 

 current and temperature holds with both these states. 



It might be argued that the mean energy of 6*5 X 10~ 10 

 ergs per ion was due to ions originating outside the cathode 

 dark space and falling through a greater potential than 

 252 volts. In order to gain this energy a fall of about 

 400 volts is necessary, and since the potential gradient out- 

 side the cathode dark space is considerably smaller, these 

 ions would have to pass a distance much greater than the 

 width of the dark space to gain this energy. The frequency 

 of collision in the comparatively high pressures used makes 

 the acquisition of energy in this way very improbable. 



§ 7. In the case of the anode, lower temperatures prevail 

 for the same current. A current of 0051 amp. produced 

 an excess temperature of 6°'9 C. in air at 2*7 mm. pressure. 

 At this temperature the loss of energy per second was 



1'9 X 10 6 ergs. 

 If each negative carrier ionizes, then 



ra = l*6xl0 16 , 

 and the average energy per carrier is 



1-2 x lO" 10 erg, 



corresponding to a fall of potential of about 80 volts, much 

 greater than the anode fall of potential, which js about 

 24 volts in air. 



If onlv a small fraction of the negative carriers ionize, 

 then the negative ion must fall through about 40 volts in. 

 order to account for the heating effect, and this potential 

 drop is still greater than the anode fall. Thus though the 

 cathode fall is able to account for the heat energy given to 

 the cathode, the anode fall alone cannot do so for the 

 anode. 



§ 8. Summary. — 1. There exists a linear relationship be- 

 tween the current through a vacuum-tube and the heat 

 energy communicated to the cathode both for normal and 

 abnormal cathode glow. 



2. There exists a pressure at which this effect is a 

 minimum. 



3. The ratio between the positive and negative carriers at 

 the cathode is approximately 10 : 1. 



4. A linear relationship between current and heat energy 

 exists at the anode — though for the same pressure and 



