Potentials due to Moving Electric Charges. 137 



Thus we have determined the scalar potential and the 

 components of the vector potential at P. These expressions 

 being true for every point and for every distribution of 

 moving electricity, it would seem to follow that for a single 

 charge e at Q moving in any manner the scalar potential at 

 any point P is 



eu 



Zirc 



and the components of vector potential 



e u 



"y 



^Kl-?)] ^lo g ^ : [,(!--)]' 



e u u. 



wio g ^i;[,(i- ? )] 



If the square of - be neglected, we get 



47rr(l-^)' 47rcr(l-^) 



e u t 



47rcT^l--^y lircrll-^) 



Though I have some misgivings as to the validity of the 

 last step of the above argument, I think the expressions 

 given have some advantages over those obtained from them 



by neglecting the square of -. Take the case of a point 



charge e in uniform motion in a straight line. If the 

 potential be taken to be 



it will be found that the potential at any point in the line 



is i— > where a is the distance of the point from the 



moving charge. Thus this potential is independent of the 

 velocity ; but it would seem that, if the velocity approaches 



