Motion of an Electrified Sphere. 617 



sero. The formula for the surface density of electrification 

 at any time is 



4ttc7=4— y"cos0 (20) 



a 2 a A v J 



But 



and finally, when m is nearly zero, 



4mr= L - 3» coa (l- e -*■ cos ^Y) • • ( 21 ) 

 a 2 6? \ a\m ) J x J 



A constant surface density fas regards time) is therefore 

 speedily established, with a term involving the first zonal 

 harmonic. Initially, the value is 



a = e/Aira 2 , 

 as it should be. 



But the infinite acceleration with m — again appears, 

 although it may be formally shown that these are the only ex- 

 pressions capable of satisfying all the hypothetical conditions. 

 The motion does not seem, therefore, to be physically likely 

 to occur, and the results serve to indicate that an assumption 

 of perfect conductivity with the ordinary condition cannot 

 readily be justified in an accelerated system, and is of a very 

 artificial character. That the electrical motions of the con- 

 ductor should be confined to the surface in this case is very 

 unlikely, and in the case of a single electron, it is difficult to 

 find a physical meaning for the assumption. 



In the more difficult case in which the sphere has a steady 

 motion on which a longitudinal or transverse acceleration is 

 superposed, a calculation of the electrical inertia on the basis 

 of the two usually adopted surface conditions on]y lends to 

 two values which must be regarded as somewhat arbitrary, 

 and although one formula may be more supported by, for 

 example, the experiments of Kaufmann, than the other, it 

 still remains as but one of many perhaps equally likely 

 results. The agreement with experiment may indicate that 

 the proper vector has been made continuous, but not that it 

 is zero inside the conductor. Yet in the present state of the 

 theory, it seems necessary to emphasise Walker's contention 

 that the Newtonian type of analysis affords the safest mode 

 of attack on the problems of accelerated motion. 



The contracted electron is rejected by Walker as having 

 no apparent dynamical foundation, but this may be only 



