produced by Motion in the Electric Field. 13 



so that 



-4™A=*\ A- K — 1 



V i? dz^afi + if + Zi* 



The displacement across any spherical surface must = <?, so 

 that 



§(xf+yg + zh)d$ = ae ; 



and therefore, if u < v, 



kT sm0d0 





,2\-i 



Thus the lines of magnetic forces are circles round the axis 

 of £ and the magnitude of the force equals 



coesm 



™V-$) 



^{(l-^sin^V 



which is Mr. Heaviside's result. If co > v, the integral becomes 



infinite, the displacement will be within a cone of semi-vertical 



v ' 

 angle sin -1 — =/3; we must therefore only integrate within 



this cone, and the equation to determine k is 

 , ziain-i^ sin 0d# _ e 



4 •(i3p*)' = (^!f 



or 



0)6(1 o ) 9 



cos/3 V w 2 / 



Thus the magnetic force 



_ -(i-ff(i-^y 



COS j8 ? l2 ( 1 g Sm ^ ) 



