( 356 ) 



plicated. The expressions for tiiis are derived in my lirsl i^aper and 

 may be derived more easily by the present method. 



§ 4. The ^peld of stationary motion especially luith a 

 velocity exceeding that of light. 



In my lirst paper I have applied the foregoing representation of 

 the field in order to tleri^'e tiie well known approximate formulae 

 of LiÉNAiiD and Wieciiert for the field at a great distance of an 

 electron moved anyhow. It strikes us in these formulae, that the 

 cases of velocities smaller or greater than that of light seem to 

 differ from each other only by the sign, wliereas in reality a funda- 

 mental physical difference must exist between the two cases: If the 

 velocity is less than that of light, Ihe whole surronndings of the 

 electron is seized by (he effects of the moving electron, if (he velocity 

 exceeds that of light, only those points are seized which lie in the 

 "shadow of motion" of the electron so to speak. This incongruency 

 is cleared, if the roots of equation (11) are discussed, what was not 

 sufficiently pointed out in my first paper. 



In general we note this (details depend on the special character 

 of the motion). If velocity is less than that of light, each of the 

 equations {\\) always has a positive root; if the velocity exceeds that 

 of ligh(, imaginary and nega(ive i'00(s are ])Ossible as well; they 

 appear in all those points A^hich are situated so to speak in the 

 front of the electron ; positive roofs exist only for those points that 

 lie in the shadow of motion ; and here for each of the equations 

 (11) even a pair of positive roots exist. Only for a narrow region 

 bordering on the shadow of motioji and about equal to the diameter 

 of the electron we have not two but only one pair of posidve roo(s. 

 It follows : The approximate formulae mentioned before, which I 

 have derived formerly supposing two roots Tj t^ to exist, hold good 

 absolutely if the velocity is less than that of light; in the opposite 

 ease they are to be replaced by out of the shadow of motion, 

 and they are to be completed by a member similarly formed within 

 the shadow of motion. 



Fig. 2 explains, what shadow of motion 

 means. Here the momentary position 

 of the electron and its preceding path OP 

 is marked. Round every point P of the 

 path the sphere may be constructed with 

 the radius cr, where t denotes the time, 

 in which the electron gets from that 

 Fig. 2. point to 0. The envelope of these spheres 



