188 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



Inspection shows that this secures the continuity of the tangential component of 

 electric force at r = a. 



The discontinuity of tangential components of magnetic force determines the 

 surface current which is due to the rotation of the uniform surface charge cr = ef4ira 2 

 rotating with the sphere. 



Thus the angular velocity round the x axis from OY to OZ is given by a> where 



or in virtue of (2), - O 1 (x*-*"-*") ...... '. - (3). 



The tangential component of electric force from OY to ( )Z is 



Thus the total moment of the couple on the sphere, which is JcrTa sin 0<IS reduces to 



and this is the rather reaction on the sphere. 



The motion contemplated may he originated by an extraneous electromagnetic 

 disturbance, in which case our conditional etpaations would have to be slightly 

 modified. But for clearness it is desirable to suppose that the sphere is acted on by 

 a purely mechanical couple of magnitude L. Hence, if the sphere is uniform and of 

 mass in, the equation of motion is 



or p 



ml^+f^(a x " + x ')=L ........ (4). 



\M 



The equations (l) to (4) determine the motion, and may clearly be presented in a 

 purely dynamical form. 



The case of uniform rotation presents no special interest here. Passing to the case 

 of a constant external couple, it appears that a uniformly accelerated rotation is 

 possible. Without entering on algebraic details, we find that 



constitutes a solution which satisfies all the equations. 



