Effects 'produced by the Motion of Electrified Bodies. 231 



hence 



4f = *£-#_!, 



dt ~~ 4z7r dx 2 p 

 dg _ ep d 2 1 

 dt ~ 



(1) 



47r dx dy p 

 dh _ ep d 2 1 



dt 4tt dx dz p J 



Using Maxwell's notation, let F, G, H be the components 

 of the vector-potential at any point ; then, by i Electricity and 

 Magnetism/ § 616, 



F = fi^\y^dxdydz, 



G = H<)))- / dxdyck, 



H = /A 



JJ p 



7 dx dy dz, 



where u, v, w are the components of the electric current 

 through the element dx dy dz, and p' is the distance of that 

 element from the point at which the values of F, G, H are 

 required, /n is the coefficient of magnetic permeability. In 

 the case under consideration, 



7 ' -P 



substituting for -j- its value from equation (1), we get 



with similar expressions for G and H. 



Let us proceed to calculate the value of F at a point P. 



Let be the centre of the sphere; then OQ = p, TQ = p / , 



S2 



