124 L. Page — Energy of a Moving Electron. 



observer moving with it the shell should be a uniformly 

 charged sphere concentric with the electron. Let the infinites- 

 imal radial velocity of contraction relative to such an observer 

 be denoted by w' and the radius of the sphere by r'. Then 

 the Lorentz-Ein stein kinematical transformations show that, to 

 an observer relative to whom the electron and shell have the 

 velocity v, the shell will be an ellipsoid similar to the electron 



Fig. 1. 



itself, but with its center displaced relative to that of the elec- 

 tron in the positive Z direction by an amount* 



~OQ = r'—P^T^ (24) 



Nevertheless, the charge on the annular ring between the cones 

 defined by 6 and 6 + cl6 (6 being, as before, the angle between 

 the radius vector drawn from the center of the electron and the 

 Z axis) will bear the same ratio to the total charge on the shell 

 as that on the corresponding ring of the electron's surface does 

 to the total charge on 'the electron ; in other words, the dis- 

 tribution of charge on the surface of the shell will be that 

 given by (21). Consequently when the shell has contracted 

 down to the surface of the electron and has imparted its charge 

 to the same, no redistribution of electricity over the surface of 

 the electron will be necessitated. 



* If the shell were not contracting it would be concentric with the elec- 

 tron. The eccentricity of the contracting shell is due to the smaller velocity 

 on the front, and greater velocity on the back of the shell. 



