612 Dr. J. W. Nicholson on the Accelerated 



placed in a uniform field, it moves in such a way that its 

 charge remains uniform. But his investigation does not 

 take account of the initial conditions of the motion, and it is 

 by no means obvious that the effect of these conditions 

 would vanish in the same way as for a sphere with both 

 electrical and Newtonian inertia. 



Let ? denote the displacement, at time t, of the centre of 

 a sphere of radius a initially placed in a uniform field of 

 electric force F of small magnitude, so that F 2 can be 

 neglected. F and f are both measured along the axis of z. 

 The uniform charge initially present on the sphere is e, and 

 (#, y, z) denote the coordinates of a point referred to an 

 origin instantaneously coinciding with the centre of the 

 sphere, r being the distance of this point from the origin. 

 Then, within the region defined by r = ct + a, Walker shows 

 that the components of the electric and magnetic forces are 

 given by 



(X, Y, Z)-£ 0, y, z) + CO, 0, 1) { F -J (ry+rtf+X-f) 



+ J (*> * *) { -V + artf + 3 (x - f ) ) - 



(«,A7)-3<y,-*0)(r X " + «') (1) 



where % denotes %(c£ — r), and c is the velocity of radiation. 



v and — are small after the manner of F. 

 * c 



The surface condition is taken to be the continuity of 



(X, Y, Z). Whether this or the more probable (X f , Y',' 7J), 



the electromagnetic force, is to be continuous does not matter 



in the present case, as they only differ by an order F 2 . The 



surface condition yields, if % = ct—a, and if the tangential 



component is zero inside, 



J*i**iMK- • • • » 



and the surface density is found to bo given by 



leading to a mechanical force on the sphere of magnitude 

 \\a 



•F-!£x"(*-a) (4) 



