[ 483 ] 



XLII. A Method of finding the Scalar and Vector Potentials- 

 due to the Motion of Electric Clia7 % ges. 



To the Editors of the Philosophical Magazine. 

 Gentlemen. — 



PROFESSOR A. ANDERSON has published in No. 236 

 of the Philosophical Magazine (August 1920) " A 

 Method of finding the Scalar and Vector Potentials due to 

 the Motion of Electric Charges." He obtains divergent 

 results from those obtained by myself in 1898 (Eclairage 

 Electrique, tome xvi. p. 5). I have no observation to present 

 for the calculations of the beginning, but I do not agree 

 with Professor Anderson when he states the following 

 proposition : — 



«H A= CCC pd^dy'dz' then 1 _^A wil] van . sh 



JJJ r [l-- p ] ' 9< 



at any point P where there is no electricity." 



For that, it should be necessaiy that the elementary 

 volume dx dy dz and the electric charge be carried by 

 the same motion ; which is not the case. 1 -n 2 a 



In addition to this, it is easy to show that V 2 A — 5 -^^r 



J c 2 at 2 



will not vanish. In order to simplify the writing, I will 

 suppose that u is constant as regards its magnitude and 

 direction, in all points and at any time. In this case 







(x-x't 



(Vf",-|-S«,(,r-x')] 



Bp -T* + Z(x-*y-^u I { X -x')+ 1 [r 



be" 



a 



■ 2 [,•-*>,(,-,*•') 



(x-x'y]Zu x (x-x' 



+/» 



[- 



1+ 



o 





7 -2M X (# 



[,.-h.,. 



■*') 



') ! 



"" ,r '~\~ 



- Idx'dy'dz'. 



J * 



