Mr. A. Schuster's Electrical Notes. 19 



should vanish, its components become determinate in every 

 respect. 



Returning for a moment to the investigation which has led 

 to equations (10), we may write the vector potential due to a 

 conduction current 4-7T through a linear element ds at the 

 origin, the currents being completed by displacement cur- 

 rents : — 



»-—G +*)-(£ 



d 2ttx \ , 

 dx r J 



G=2ircfoH? 



r s 



d 27TX 7 



— as ; 



dy r 





d 2ttx , 



— j ds. 



dz r 



As far as the magnetic forces are concerned, the terms in- 

 volving the differential coefficients disappear, and we might 

 put equally well 



Y ^jrds_ G H = 



r 



If the conduction current is i instead of 47r, we obtain 

 ¥=*—, G=0, H=0; 



and this is exactly what we should have obtained if we had 

 neglected the displacement currents altogether : a well- 

 known result. 



The following transformation seems of some interest. Con- 

 sider electric currents in a system of bodies whether con- 

 ductors or non-conductors, the magnetic permeability being 

 uniform for the sake of simplicity. The Vector Potential at 

 a point x, y, z will be 



-M 



- da db dc 

 r 



where the currents are given as functions of a, 6, c. 



Assume further the existence of a current function, from 

 which the currents may everywhere be derived. Over certain 

 surfaces the current function may be discontinuous. We put 

 therefore 



dd> dd> deb 



u= £> v =w w= ck> 



and form the equations for the components of magnetic 



C2 



