214 Prof. L, T. More on the 



If y is the displacement by the electric field, E, 

 2, the displacement by a magnetic field, M, 

 [Xq, the electromagnetic transverse mass of an electron for 



velocity zero*, 

 V, the velocity of light, 

 e, the electric charge on the particle, 



then « E 1 



y ~ ^ V 2 /3 2 <P(/3)' 

 and 



- .£ M 1 

 where as before, 



a>f*\ 3 1/1 + /S 2 , 1 + /9 ,\ 



Abraham 



<J)( / 5) = (1~/3 2 >I ~ 2 , .... Lorentz-Einstein 



<I>(/3)^(l-./3 2 )~* Bucherer 



According to these theories, when /3 = 1, 

 <|>(/3)=ao, and y=z=0 ; 

 and when /3 = 0, 



<!>(£) = 1, and y = z=oo. 



All theories agree, that an electrified particle, moving with 

 the velocity of light, cannot be deflected by an electro- 

 magnetic field, and this coincides with the idea that the 

 electromagnetic mass then becomes infinite. But for a 

 small velocity these deflexions become very large and are 

 infinite when the electron is at rest. Even if we should 

 accept this result for the case of the electric displacement, 

 we should still have the difficulty of accounting for any 

 action between an external magnetic field and an electrified 

 particle at rest. These results for a stationary particle 

 are difficult to reconcile and impossible to explain without 

 making special and unlikely hypotheses for the constitution 

 of the electron. It should also be noted here, that this is 

 the only case where a small mass, whose velocity, charge, 



* It is impossible for me to form any conception of this quantity if it 

 has a Unite value, and yet it is one of the essential factors of the equations 

 which follow. In the first place, an electron at rest has no electro- 

 magnetic field ; and secondly, how can an electron with no motion have 

 a transverse mass of any sort, when that is defined as mass due to a change 

 in direction only? We might as well give a finite value to the centri- 

 fugal force of a body at rest. 



