MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 197 



coefficient that it is no longer legitimate to neglect those waves, and a uniform 

 acceleration cannot, in point of fact, be established. . 



We may further observe that an uncharged sphere of atomic size would, under 

 ordinary conditions, give fundamental vibrations of frequency corresponding to 

 extreme ultra-violet radiation, damped with exceedingly great rapidity. Our result 

 proves that, at a speed approaching that of radiation, the fundamental vibration may 

 be brought within the visible spectrum range, and at the same time the damping 

 becomes relatively small. 



A similar conclusion holds for an unconstrained charged sphere provided m'/m is 

 not large. 



These results are of significance in optical theory, and investigation of the effect 

 of speed on the vibrations, carried to a higher degree of approximation, appears to be 

 desirable. 



