required to maintain a Current in a Gas. 295 



potential in hydrogen at 10 millimetres pressure between 

 plates a centimetre apart. 



Larger differences between the sparking potential and the 

 potential required to maintain a discharge are obtained when 

 the force near the cathode is again increased. If the force 

 be 200 volts per millimetre in the first millimetre near the 

 cathode and 40 volts per millimetre for the rest of the 

 distance, then the values of a 1? /9 1? a 2 , and fi 2 are 



^ = 28, a 2 = 2'0, 



ft= -9, &=0, q.p. 



In the same manner as before the value of a may be found. 

 In this case a = 4"25 millimetres, and the fall of potential 

 between the electrodes is 200 + 130 = 330 volts, whereas the 

 sparking potential for the distance 4*25 millimetres between 

 the plates is 385 volts. 



The same analysis shows that if the force is 200 volts per 

 millimetre in the first millimetre and 30 volts per millimetre 

 in the rest of the path of the discharge, the current would be 

 maintained if the distance between the plates is 9 millimetres 

 so that the total fall of potential between the electrodes would 

 be -140 volts, whereas the sparking potential for the same 

 distance and pressure of gas is 545 volts. 



Similar results may be obtained by using the values of a 

 and {3 which have been found for air. 



Thus it is evident that the more the force near the cathode 

 exceeds the force in the other parts of the discharge, the less 

 will be the potential required to maintain the discharge, 



5. The first example which has been chosen shows that a 

 potential of 560 volts is sufficient to maintain a discharge of 



1 centimetre long in hydrogen at 10 millimetres pressure 

 when the force is uniform and equal to 80 volts per milli- 

 metre in the layer two millimetres thick near the cathode, 

 and 50 volts per millimetre in the remaining 8 millimetres 

 of the path of the discharge. It is easy to show that the 

 same field of force reversed would not suffice to maintain a 

 discharge, the larger force being then confined to the layer 



2 millimetres thick in contact with the positive electrode. 

 This may be seen bv substituting the following values of 

 *i, A, « 2 r &, a> and b :— 



ai = 3-6, « 2 =10*0, b= *8, 



& = -021, /3 2 = -081, a = l-0, 

 in the expression 



-&€<**-* » /3 2 -a 2 e ( ^- a * )(fl - fe) 



