[ 175 ] 



XVII. llie Spheroidal Electron. 

 Bi/ Prof. A. Anderson*. 



ON the supposition that the shape of an electron in motion 

 is a spheroid, the direction of motion being along the 

 axis of symmetry, and the charge on the correlated electron 

 being distributed on its surface as if it were a conductor at 

 rest, the values of the momentum and energy in the gether 

 can be calculated. The length of the semi-axis in the direction 

 of motion is 1>, and that of the semi-axis at right angles to this 

 is a : b is thus the contracted length, or the length of the 

 semi-axis in the direction of motion after it has suffered the 

 Lorentz-FitzGerald contraction. As usual, /5 denotes the 



quantitv (1— 2 I , where v is the velocity of the electron 



and c the velocity of light. 

 The results are, if fib>a. 



momentum . 



M=_ e*/3v r 2/3 2 b 2 -a 2 1oo , /3/> + (/3 2 A 2 -q*)- 



1 6ttc 2 (/3 2 b 2 -a 2 ) h L /3 2 b 2 - a 2 ' ° g £/, _ (j&p _ tff 



2 13b - j 



(!3 2 b 2 -a 2 )*J 

 and energy 



If '&b<a, 



+ — -7, — ™nr tan 

 and 



a 2 -/3 2 b 2 a /3b 



1 ' $7rc 2 (a 2 -l3 2 b 2 yi(a 2 -/3 2 b 2 )> 



" ]• 



* Communicated by the Author. 



m 



