Properties of the Electric Field. 171 



iron : hence, since the tangential momemtum is constant, 



In other words, the normal induction is constant. Hence 

 we have arrived at the usual boundary conditions for the 

 lines of magnetic force. 



The intensity of magnetization at the surface is 



where t and t x are the tangential velocities of the tubes in 

 air and iron respectively. 



That, from this point of view, magnetization corresponds 

 to a discontinuity in the tangential velocity of the tubes of 

 electrostatic induction. 



We can easily prove from this consideration that if the 

 lines of flow of the tubes coincide both inside and outside the 

 cylinder with those due to a solid cylinder moving vertically 

 through an incompressible fluid, the distribution of magnetic 

 force will be that produced by the cylinder, if uniformly mag- 

 netized in the horizontal direction. 



We have not hitherto determined the velocity with which 

 the tubes of electrostatic induction are moving. We may, 

 however, easily do this when the electromotive intensity is 

 entirely due to the motion of the tubes. For, in this case X, 

 the x component of the electromotive intensity, is given by 

 the equation 



= 47T/-6 \ iu(ivf— uh) — v (ug — vh) \ , 



= 47T/* { (u 2 + v 2 + w 2 )f— u (uf+ vg + wh) \ , 



with similarly expressions for Y and Z. 

 Since 



4tt v 4-7T v 4tt 



X=£.A Y =x^ K ' 



9 1 9 1 9 *- 



u- + v + t o-= fiK , 



and uf+ vg + wh = . 



Hence, in this case, the tubes are moving through the medium 

 at right angles to themselves with the velocity of light. 



we see 



