ELECTROSTATIC FIELD IN VACCIM TUBES 



305 



the case of thick grid wires in terms of exi)ansions in series of elli[)tic functions 

 were discussed by Knight, Rowland and McMullen**-'". The prol^lem of a 

 finite number of grid wires was treated by Barkas". More recently tubes 

 with close spacing between grid and cathode, but with anode and grid as- 

 sumed far apart, have been analyzed in terms of elementary functions by 



0.05 O.iO 0.(5 0.20 0.25 0.30 0.35 0.40 0.45 0.50 



DISTANCE ALONG CATHODE, X/g 



Fig. 2— Variation of amplification factor along the cathode surface of a triode. 



Fremlin'2. A solution based on the Schwartz-ChristofTel transformation 

 has been given by Heme" for the case of grid wires of finite size and approxi- 

 mately circular in shape. 



Since the derivations have been adequately covered in the references cited, 

 we merely state the final formula here and indicate how it may be verified 

 as correct. Let V{x, y) represent the potential function corresponding to 



