834 Accelerated Motion of a Dielectric Sphere. 



uniform motion, and an accelerating force is applied per- 

 pendicular to that motion. Now Walker has shown in the 

 case of the conductor, that when the surface condition is 

 the evanescence of the tangential electromagnetic force, 

 Abraham's expression does not follow as the result of a 

 direct calculation from the primary electromagnetic equa- 

 tions. This disproves the quasi- stationary principle for the 

 initial motions of a conductor at least, although the initial 

 condition, involving the instantaneous creation of a uniform 

 field, is somewhat artificial. 



The equations valid for a dielectric in variable motion are 

 not yet free from doubt, and a direct calculation of the 

 inertia in this case, as Walker points out, is not at present 

 possible ; but he concludes that the inertia of the dielectric 

 with a large value of k would be practically the same as for 

 a conductor with equal charge, by the following argument *. 



" Since there is continuity of normal flux of disturbed 

 electric force at the surface, the functions which determine 

 the disturbance inside the sphere are of order /c' 1 as com- 

 pared with those which determine the outside field. Hence 

 the tangential component of electric force inside, and there- 

 fore also outside, is very nearly zero. Thus since the equa- 

 tions for the aether are not modified by the motion of the 

 sphere, the equation of motion and the surface forces outside 

 differ by terms of order k~ 1 from those for a perfect con- 

 ductor. If this argument is valid, the assumption of perfect 

 conduction, or of a high value of k for the charged particle, 

 would equally well explain Kaufmann's results, and give the 

 same value for the electric inertia without limitation as to 

 speed." 



This argument appears to dispense with the necessity for 

 complete analytical treatment. The inertia in question is that 

 derived by Walker's analysis of the conductor with the other, 

 and in the opinion of the writer, less likely condition in that 

 case, that the tangential electric force is zero. Quoting the 

 results, the initial longitudinal inertia becomes 



<? | 4_5p + 4# . 4-13P + 6F ) , m 



16ac 2 \ F(l-P)i- sm k F(l-P) j' * { } 



and the transverse inertia is 



e 2 r 4P-1 . ... , 1 + 2P \ /1Q . 



so^\ k\i-pf m ^+-^-j;'- ■ • ( 18 > 



and these are the initial values to be regarded as true for a 

 * Phil. Trans. 1910, A, p. 178. 



