16 Mr. A. Schuster's Electrical Notes. 



may be effected in a number of different ways. For instance, 

 we may make 



*-£§' Gi=0 ' Hi=0 ' 



dV 



when V is defined by (f> = -y- . 



In this case the currents are completed at the origin by a 

 flow parallel to the axis of X. 



As regards the surface conditions to be satisfied by the 

 vector potential, there seems no difficulty when the magnetic 

 permeability is uniform throughout space, but for the surfaces 

 of two media having a different permeability special conside- 

 rations seem necessary. I am not aware that this point has 

 been investigated. 



If the medium through which the currents flow is subject 

 to magnetic polarization, we may write for the vector potential 

 at the point a, y, z, 



¥=ftj- r d«/dy'dz' + jJJ(B J, - G^dx' dy' dz\ (14) 



where the components of the currents are functions of x' y f z' 

 and p is the reciprocal of the distance between x, y, z and 



<*///. _ _ 



A, B, C are the components of magnetization of the medium, 

 [f these are due to the distribution of currents alone, we have 

 the additional equations 



A = Ku, B = k/3, C = fcy, 



a, /3, 7 being the components of magnetic force. Integrating 

 the second term of (14) by parts and substituting 



_dy__d/3 

 dy dz ? 



the equation for the vector potential is obtained in the form 



F = (T( ^ dx' dy' dz 1 -r ffi (Bn - Cm)dS, . (15) 



when /u,= l + 47r/e and /, m, n are the direction-cosines of the 

 normal drawn towards the outside of the element dS, the 

 surface integral being taken over all surfaces at which two 

 media of different magnetic properties join. 



These equations differ from those given by Maxwell by the 



