72 THE THEORY OF IONIZATION OF GASES 



the quantity No) by the increased activity of the positive 

 ions at the negative electrode. 



30. Comparison of the effects of concentrating the 

 force near the cathode and near the anode ; 

 explanation of sparking potentials for positive 

 and negative points. 



It is interesting to examine the equation 



i ft 



more generally and to contrast the effects of increasing 

 the force in the parts of the field near the cathode and 

 near the anode. 



For a field of force chosen arbitrarily the sum of the two 

 fractions in the above equation has a value Y which is 

 different from unity. When the values of a and are 

 small, the forces do not suffice to maintain a current, 

 and each of the fractions becomes equal to unity, so that 

 Y=2. As the values of a and /3 increase the fractions 

 diminish, and their sum becomes equal to unity when 

 the forces are sufficient to maintain a discharge. Hence, 

 when the value of Y lies between 1 and 2 for a system 

 of values of a and /3, the forces between the electrodes 

 will not suffice to maintain a current. 



The effect of reversing a field may be found by inter- 

 changing ai and ft, and a 2 and /3 2 , and if this be done in 

 the two numerical examples given above, it will be found 

 that Y is greater than unity in each case, so that when 

 the forces are reversed they are not sufficient to maintain 

 a current. 



A very simple case arises when one of the forces X 2 , 

 acting through the distance &, is so small that the 



