SPARKING POTENTIAL IN A UNIFORM ELECTRIC FIELD 55 



Exactly similar phenomena are observed when the 

 discharge takes place through a gas in the space between 

 two coaxial cylindrical electrodes : for pressures above 

 the critical pressure it is easier to produce a spark when 

 the inner cylinder is negative, and for lower pressures 

 the smaller sparking potential is obtained when the 

 inner cylinder is positively charged. 



23. Condition for sparking in a uniform electric field. 



The sparking potential between parallel plate 

 electrodes can be deduced immediately from the formula 



/ _m e (a-/3)Z 

 n=W(A^ 52L - __, already obtained in section 18, 



which represents the number of ions n reaching the 

 positive electrode when no negative ions are started by 

 ultra-violet light from the negative electrode. The 

 quantity n increases as the distance I between the plates 

 increases, the force X being maintained at a constant 



value, and when /3e^ a ^' becomes equal to a the 

 denominator of the above fraction vanishes, and n becomes 

 infinite. A current will therefore continue to flow for an 

 indefinite time after the light ceases to act when the 

 distance between the plates attains the value S given by 

 the equation 



Thus the sparking potential S X is known for the 

 particular distance S and pressure p of the gas. 



In order to test the theory experimentally, the sparking 

 distances S corresponding to given values of X and p 



were found by means of the formula S= ^ log l~ 



