ELECTRON STREAMS IN A DIODE 847 



form (53), with the values of the starred coefficients abbreviated and as- 

 sembled as follows: 



ai = 1 - e~^ - ^e~^ 



a2 = 1 - c~^ (63) 



A* = 



2e^ 



az= 2 - 2e~' - ^ - ^e~^ 





D* 



2^ 



2^ (C/„ + U,) 



E* = 4- [Ui - aUa + Ui;)]e-^ (64) 



'■'UH^)"-' 



G* = - -^ [(ai - 0:2^) C^6 - ciiUa + «ir(£^a + C/ft)] 



H* = 



Ub 



With the exception of a difference in symbols, these coefficients are iden- 

 tically the same as those obtained by Llewellyn and Peterson^- ^ from cal- 

 culations on the motions of electrons as individual particles, and this cor- 

 respondence apparently reconciles the wave theory and the particle theory 

 of electron streams. The correspondence is largely the result of a new 

 feature in the wave theory, that is, the expression of the electron stream 

 as the sum of two components, a wave traveUing with a finite velocity and 

 an oscillation that is in phase over the entire diode space. 



Llewellyn and Peterson have derived the circuit equivalents of electronic 

 tubes from the values of the starred coefficients, and these equivalents are 

 well known in the electronic art.* The present section confirms these rela- 

 tions, as derived for an ideaUzed electron stream. The validity of this 

 idealization is considered in the following section. 



