662 BELL SYSTEM TECHNICAL JOURNAL 



as we have done previously. This merely means letting 



r =i/3 (16 1) 



The following nomenclature will be used 



Ji , Ji d-c current densities 



Ml , Ms d-c velocities 



Poi , Po2 d-c charge densities 



POI = —J\/U\ , Pj2 = —Jllu-i. 



Pi , p2 a-c charge densities 



I'l , Vi a-c velocities 



Vi , Fi d-c voltages with respect to the cathodes 



V a-c potential 



^1 = Cj/Wi , ^2 = w/M2 



From (2.22) and (2.18) we obtain 



and 



(16.3) 



It will be convenient to call the fractional velocity separation b, so that 



«i -f Ma 

 It will also be convenient to define a sort of mean velocity Mq 



u, = J^. (16.5) 



«1 -H Mj 



We may also let Vt be the potential drop specifying a velocity uo , so that 



Mo = \/27jFo (16.6) 



It is further convenient to define a phase constant based on uo 



CO 



(16.7) 



We see from (16.4), (16.5) and (16.6) that 



)8i = /3.(1 - b/2) (16.8) 



0i = /3.(1 + ^>/2) (16.9) 



