830 Dr. J. W. Nicholson on the 



second paper, although the special case is not examined. 

 Let e be the charge on the sphere of radius a, k its dielectric 

 constant, and c', c the velocities of radiation inside and out, 

 so that 



KC' 2 = C 2 . (1) 



f is the displacement of the sphere at time t, and F the 

 force, of a mechanical origin. As for the conductor, the 

 field outside can be expressed in terms of a function % (ct— r), 

 small like F, in the form, valid for a certain region, 



(X, Y, Z) = « (.,, y, z) + e ? (- 1, 0, 0) (r> x " + rx> + x - f ) 



+ ™(.,,y,c)(,.y' + 3r X ' + 3 x -3 e |). . . (2) 



Inside the sphere, since there is no initial field, we may 

 write, in terms of functions fa (c't— r) and fa (c'i-f r), both 

 of which are required, 



(X, Y, Z)= i(-l, 0, 0){>W + t2") + '-(f i'-+V) + + 1 + *.} 



C X 



+ ~ (.r, y, z){W + *,") + 3r(*,' -f ,') + 3(*, + f s ) }, (3) 



the axes moving with the sphere. In order that the internal 

 field may be finite at the centre, 



fa(c't)+fa(c r t) = (4) 



The tangential electric and electromagnetic forces are 

 identical to the order contemplated, and thus by the con- 

 tinuity of either at r = a, 



(a 2 X'' + a X' + X-~)=c'{ a Xfi' + t2') + a(fi-f*) + fi + ^}- ( 5 ) 



The difference of normal flux being 47rcr or e/a 2 , it follows 

 that 



o («%' + %- 7) =«c'(afa'-afa' + fa + fa). • (6) 

 A determination of the mechanical force gives * for its 

 * Walker, I c. p. 174. 



