Accelerated Motion of a Dielectric Sphere. 829 



perfect when its motion is accelerated. The perfect con- 

 ductor of the usual theory leads to disturbing infinities when 

 it has no Newtonian mass. The indications that the mass of 

 a single electron can have a Newtonian element are not very 

 securely established ; and although certain experiments can 

 be interpreted in accordance with this view, there is always 

 a possibility of other interpretations which do not involve it. 

 For example, it is possible that the particles in Kaufmann's 

 experiments are electrons not free, but attached to matter. 

 A comprehensive examination of the conditions of motion of 

 a small body without a Newtonian mass is therefore desirable, 

 and this was made in the case of a conductor under the action 

 of a small force in the previous paper. Apart from indica- 

 tions there obtained, it seems unlikely on general grounds 

 that an electron can be endowed with properties analogous 

 to those of a conductor, for there is a difficulty of attaching 

 a physical meaning to such properties in a single electron. 

 Moreover, the rapidity of damping of the oscillations set up 

 when the motion of the conductor is changed, supplies a 

 strong adverse argument. 



Some interest therefore attaches to the corresponding 

 problem of a small sphere, with a surface charge, whose 

 interior has the properties solely of a dielectric, with no 

 conducting element. 



In the present paper, the motion of such a sphere, devoid 

 of Newtonian mass, is investigated, and it is shown to present 

 none of the difficulties noticed in the case of the conductor. 

 A small field of force can produce a finite acceleration, and 

 will give the effect of a constant acceleration after a short 

 time, if the dielectric coefficient be not too great. If this 

 coefficient is great, the oscillations initially set up are very 

 permanent, and the constant acceleration is not established 

 by a uniform field within the time during which the equa- 

 tions are good approximations to the motion. The problem 

 in this case bears some resemblance to that of the perfect 

 conductor, for the disturbance inside the sphere tends to 

 zero as the dielectric constant increases. But the problems 

 do not become identical, for in the case of the conductor, the 

 charge is allowed freedom of movement on the surface, and 

 in fact does redistribute itself in the manner previously 

 calculated. In the dielectric sphere, it remains uniformly 

 distributed, and the problem thus corresponds to those of 

 accelerated motion usually treated by the quasi-stationary 

 principle, in whose application any redistribution is ignored. 



The main outlines of the necessary analysis, when both 

 kinds of inertia are present, have been given in Walker's 



