THEORY OF ELECTRIC DISCHARGES 69 



pressure, and let a force of 80 volts per millimetre act 

 in a layer extending 2 millimetres from the cathode, 

 and a force of 50 volts per millimetre in the rest of the 

 field. The values of a b fa, a 2 , /3 2 , as obtained from the 

 curves giving a/p and fi/p in terms of X/p, are as follows : 



ai=10-0, &=-081, a 2 =3'6, ft='021, 

 so that the distance b may be found from the above 

 equation, since a is given equal to *2. The value of b 

 thus determined is 8 millimetres, and hence the total fall 

 of potential between the electrodes is 80x2+50x8 

 =560 volts, which is about 20 volts less than the 

 sparking potential in hydrogen at 10 millimetres pressure 

 between plates a centimetre apart. 



Larger differences between the potentials are obtained 

 when further increases are made in the force near the 

 cathode. Thus, if Xi=200 volts per millimetre in the 

 first millimetre of gas near the cathode and 40 volts per 

 millimetre in the rest of the field, a similar calculation 

 gives &=3'25, so that the fall of potential between the 

 electrodes is 330 volts, the corresponding sparking 

 potential between the electrodes, 4*25 millimetres apart, 

 being 385 volts. It is thus obvious, from the theoretical 

 results that have been obtained, that the potential 

 required to maintain the current in the gas diminishes 

 as the current increases, owing to the increase of the 

 force near the negative electrode. 



29. Simple experiments to illustrate the effect of 

 concentrating the force near the cathode. 



These results are in accordance with the experi- 

 mental investigations 1 for pressures above the critical 



1 Philosophical Magazine, June, 1906. 



