( 357 ) 



defines the shadow of motion. Kvidentl}- it is the snialler, the more 

 the velocity of the electron exceeds that of liglit. The region bordering 

 on the shadow of motion, wiiich was mentioned before, is also sketched 

 in the figure as a narrow strip. 



The foregoing general remarks are coi'roborated by closer discus- 

 sion of stationary motion with constant x'elocity v. The field of 

 stationary motion can be found exactly by a singular process of 

 reciprocation ') if r <^ c. What happens if v > c, has l)cen explained 

 by DES CouDREs following the steps of Heaviside. Compared to 

 DES CouDREs' treatment the following is hardly new. It may merely 

 be pointed out, that the infiniteness of the Heaviside-des Coudres '^) 

 solution near the borders of the shadow of motion is not real, the 

 formula no longer holding good in this region. The infiniteness 

 mentioned just now results from des Coudres treating the case of a 

 charge concentrated in one point, which is passing to the limit of 

 vanishing dimensions of the electron. We shall adopt in general this 

 simplification and thereby dispense with a rigorous solution, but at the 

 same time we shall point out, that this simplification is not legitimate 

 near the border of the shadow. We suppose bodily charge, as it 

 will be shown later, that in case of surface charge any motion 

 with V ^ c is actually impossible. 



Let the stationary motion be directed towards the positi\'e axis 

 of n'. The system of coordinates has its origin O at the position of 

 the centre of the electron at the time t. Let the coordinates of the 

 point in question be a', y, z, let its distance from be r =: \/x^ -\- y'^ -\- c'\ 

 so that r now has a diiferent meaning from that in § '2 and § 3. 

 At the time t — t the centre of the electron was in the i)oint — or 

 of the axis of x ; the distance of the point in question from this 

 point is 



K ^ ]/{.v + vty + y-' + Z-' (19) 



The conditions, under which the triangle (7iV^ f t) is just possible, 

 are given by the equations (11) 



Hi — a^ cr^ , A', -j- a = T„ . . . . (H) 



in the case of an exterior point (more correctly A' > a) ; ^ve can 

 combine (Jl) into 



(.^. + yry + y-' + z' =: (c t ± a)' 

 or 



^) V. the summary of H. A. Lorentz in -'Encykiopiidie der maliiemalischen 

 Wissenschaften". Bd. V. Art. i4. Nr. 11. 



2) Zur Theorie des Kraftfeldes eiecUischer Ladungen. LoRENTz-Jubelband, p. 052. 

 Haag 1900. 



