796 BELL SYSTEM TECHNICAL JOURNAL 



where / represents the variable part of the space current on the basis 

 that Jn represents the wth approximation, but that the series converges 

 rapidly so that we need consider only the first two terms to arrive at 

 a substantially accurate result. The expressions derived for the first 

 and second approximations are known to be 



/i = a,El{\ + a,R), 



/2 = 02^7(1 + a,RY, 



where the 'a' coefficients describe the tube characteristic 



/ = aiv + a^v^, 



R being the external plate circuit resistance, v the tube potential, 

 and E the circuit e.m.f. 



Turning now to the equations for the hysteresis loop branches, we 

 have from (4a) 



B = aiah — aoo^i'^ + auhH + a^^H'^- 



Hence by the analogy between flux and current, and between reluc- 

 tance and resistance, the first order terms are reduced by the factor 

 1/(1 + aiR) which corresponds to 1/(1 + XawlA), and the second 

 order terms are reduced by the cube of this factor, which yields the 

 same results (42) as the laborious direct method. 



