produced by Motion in the Electric Field. 5 



e d 1 _ j_ d_l ,_ e d 1 m 



^ ~ 47T da r' 47r c?y r' 4*7r de r " 



hence by equations (1), 



/3=-ei0 O (l+i^)^, 



y = 0. 



Thus the lines of magnetic force are circles with their centres 

 along and their planes at right angles to the axis of z. 



At a distance from the centre large compared with the 

 radius of the sphere the magnetic force is the same as that 

 due to a current ew , but close to the sphere the relative 

 motion of the sphere and aether causes it to be larger than this, 

 and at the surface of the sphere it is the same as that due to 

 a current § eiv . 



The energy due to this distribution of currents is f p. 



Another case which can be easily solved is that of a right cir- 

 cular cylinder rotating with an angular velocity g>, each unit 

 length of the cylinder being charged with E units of elec- 

 tricity. If a is the radius of the cylinder, 



a 2 y a 2 a 



/_ J? * - Ji y. 



■'~2wr 2, 9 ~~27rr 2; 

 and by equations (1), 



a = 0, 13=0, 7=-2Ew- 



a? 



V 



Thus outside the rotating cylinder there is a magnetic force 

 parallel to the axis of rotation. 



If we assume that the aether outside the sphere is at rest, we 

 can find the solution of the case of a charged metal sphere 

 executing harmonic oscillations. Suppose the sphere to be 

 moving parallel to the axis of z, the velocity at any time t 

 being represented by the real part of eoe^. Then if we take 

 rectangular axes passing through the centre of the sphere and 

 moving with it, the following equations are true inside the 

 sphere if u, v, w are the components of the current, a, b, c 

 those of magnetic induction, yjr the electrostatic potential, F, 



