618 The Accelerated Motion of an Electrified Sjrfiere. 



apparent, and certainly it does not seem possible to dispense 

 with the Principle of Relativity and its consequences. 

 Moreover, Bncherer's contracted electron gives a very good 

 agreement with Kaufmann's experiments, and it is desirable 

 that a direct mode of analytical treatment of an electron 

 which changes its shape, not associated with the quasi- 

 stationary principle, should be found, but none has been 

 suggested as yet. 



There is one combination of a small mechanical force with 

 a weak electric field which would give a finite initial accele- 

 ration to a sphere whose inertia is electrical only, no electrical 

 effect being maintained inside. This combination satisfies 

 the condition 



G=-i*F, (22) 



and the corresponding value of fis the limit of 



WF /« y g . n ct Wvl 1 *F 4 eF at 



3 v 2 m' \m'J a \mj 'dm' 3 m! c K ' 



so that the acceleration at t = is r , — .. But it becomes 



6 m' 



infinite afterwards. The surface density remains perma- 

 nently equal to 



ir(^ +FC °* e ) < M ) 



so long at least as f is small. 



In connexion with the question of electrical inertia, the 

 investigations of Conway and Walker, starting from the 

 same differential equations and surface conditions, lead to 

 different values of the transverse inertia, that of Conway 

 being identical with Abraham's expression. A comparison 

 of the two methods will be made in a later note, for it seems 

 that the formula given by Walker in this case is the only 

 possible result of a rigorous analysis applied with the vanish- 

 ing of the tangential electromagnetic force as its surface 

 condition. 



Trinity College, Cambridge, 

 1910, May 28th. 



