OI'ER.-^TION or THERMIONIC VACUUM TUBE CIRCUITS' 461 



APPENDIX I 



To Show thai with Nef^alive Grid Potentials the Relation: 



dEp dEg 

 Holds With Fair Precision 



We have the fundamental expression : 



Ip = Ip{Eg,E,) (1) 



Suppose that Eg and Ep are allowed to vary under the restriction 

 that Ip is maintained constant. Then : 



Hence : 



Whence : 



Also: 

 Hence : 



dlp = (2) 



dip n ^h , dip dEp 



dEg ^ dEg "^ dEp dEg ^^^ 



dUp = (5) 



d^P _^_ d'lp I g d'lp dEp d'lp (dEpY dIpd'-Ep 

 dEg' ^ dEg^'^dEgdEpdEg'^ dEg'UEg) '^ dEpdE/ ^^ 



Then with the aid of (4), above, and (G) in the body of the paper, we get 

 9m 9m I dEp 



wr^dEp+dE}^"^ ^'^ 



Equation (7) shows that 



provided that : 



when Ip is constant. 



9At ^ 9m /gx 



dEg dEp 



d^Ep 

 dEo- 



= (9) 



Experimental curves showing the relation between Ep and Eg 

 required to maintain Ip constant are straight lines, to a very close 



