2 Mr. J. J. Thomson on the Magnetic Effects 



placement-currents are due entirely to variations in the electric, 

 displacement (/, g, h) caused by the motion of the sphere and 

 the medium, the components f l7 ^ l7 £i of these currents would 

 be given by 



df , df , . .df 



da da , , da 



dh dh , . dh 



^ = U dx +V dy +{w - W ^d- Z - 



These values, however, do not satisfy the equation 



dx dy dz ' 



unless the dielectric is moving uniformly; so that, if the 

 circuits are to be closed, the motion of the medium must 

 produce some other effect analogous to a current. 

 Since 



<^?i , dVi &K\ _d / Au du j du\ 

 dx dy dz dx \ dx ^ dy dz ) 



d ( Av dv 7 dv\ d ( dw die , div\ 

 + dyVd X +S dy +h dz) + TzVd^ +y d^ + h di)' 



we see that the currents will be closed if we add on to the 

 components f 1; rj l} Ji the components | ,?o> /°o> where 



„ „du du , du 

 -^=- f T X + VTy +k dz> 



.dv dv , 7 dv 



- Vo= - f dl e + ^ +h Tz> 



4, „clw div , , dw 



The medium is assumed to be incompressible, so that 



du .dv dw _ n 

 dx dy dz 



Hence the components of the total effective currents are 



