VACUUM TUBE ELECTRONICS 83 



merit components of the current in the neighborhood of the grid wires 

 have been done away with. 



The appHcation of the equations to this special case is dealt with 

 in the section of this paper devoted to positive grid oscillators. Be- 

 fore these oscillators can be treated comprehensively, a further exten- 

 sion of fundamental theory is necessary. This extension comes about 

 because positive grid oscillators are often operated with a slightly 

 negative potential applied to the plate. 



VI. Triodes with Positive Grid and Negative Plate ^ 



When consideration is directed to tubes operating with positive 

 grid but negative plate, the fundamental underlying theory must again 

 be investigated. The reason for this lies in the fact that all electrons 

 which penetrate through the meshes of the grid are turned back be- 

 fore they reach the plate, so that in the grid-plate space there are two 

 streams of electrons moving in opposite directions. The effect of this 

 double value for the velocity may readily be calculated in so far as 

 direct-current components, only, are concerned. We have merely to 

 note that the charge density is double the value which it would have 

 in the presence of those electrons which are moving in one direction, 

 only, so that the correct relations are obtained from the equations al- 

 ready derived by taking twice the value of direct current in one 

 direction. 



When alternating-current components are considered, however, 

 matters are more complicated, but not difficult. To see what the 

 actual relations are, let there be two possible values at any point for 

 the instantaneous velocity, and call these two values Ua and Ub, respec- 

 tively. Then the relation between force and acceleration becomes 



eE^dUa^dlh . . 



m dt dt ' ^ ^ 



Hence, at a given value of x we have by integration 



Ua = Uh -\- constant. 



But, when both values of velocity are separated into their components 

 according to (5) we have from (39) 



Uao -\r Uai -\- • • ■ = Ubo -\- Ub\ + • • ■ + constant. 



^ Since the publication of this paper in the Proceedings oi the Institute of Radio 

 Engineers, several questions have l)een raised regarding the treatment presented in 

 sections VI and VII. These are being investigated and will form the basis of 

 another paper. 



