( 339 ) 



l)()tli the roots arc positive if 



V ,v zp a c 

 c' — v^ 



tliej are negative, it' 



V X zp a c 



>0, i. e. 



<± 



< 0, i. e. .V > ± — . 



Evidentlv the phines .i' = ± - are polar planes of the points P^ i\ 



with respect to the surface of the electron. We distinguish a back 

 and a front of these planes judging from the direction of motion. 



Fig. 3. 



Fig. 3 gives the result of our discussion. Here the points P^, P, 

 and their polar planes are constructed. From P^, P^ the cones 

 K^, K^ diverge, which touch the surface of the electron at its inter- 

 section with E^ E.^; thej appear in the figure as two pairs of straight 

 lines. We call such points region 1, for which both pairs of roots 

 are either Imaginary or negative. Region II consists of such points, 

 for which only one pair of roots (tJ is positive. Finally region III 

 is that, in which both pairs of roots are positive. The regiojis I, II 

 and III are distinguished in the figure by different shading. We 

 need not concern ourselves with the interior, where the field acts 

 differently. 



We now proceed to the computation of the scalar potential. 



If V <^ c, we get on account of the existence of a positi\'e root 

 T, and Tg (see (13) and (14)) : 



*"'' = 5 ƒ 





(23) 



Here we introduce the variable 



