Recent Theories of Electricity. 211 



From J G | , be finds that 



»'=S5V»tt+tf , +* 8 '+ } 



and „ 



m"=g^y 2 {(l + i) + Q + ^ 2 + a + f)^' + }• 



For a stationary electron, 



£ = and m r = m" = 



m + m 2 " 



= k 



and —^ 

 m 2 





m 





If the velocity becomes that of light, 



fi — 1 and m'=m" = x>. 



For intermediate values of /5, m f >m" . 



Kaufmann,byan ingenious experiment, tested the increase 

 of the apparent transverse mass with the velocity of radio- 

 active particles and found such an increase. 



If m/' and m 2 " are the transverse masses of two particles 

 at different velocities, we may put 



Then 



Now by his experiments tc and k are equal, within the 

 limits of accuracy ; since m" remains finite until the velocity 

 of light is reached, w? must be excessively small and is now 

 taken by writers on theory to be actually zero. Although no 

 experiments have been made on the longitudinal electro- 

 magnetic mass, the same is held to be true for it. 



Other theories of the nature of the electron are essentially 

 the same. They present, however, some important differ- 

 ences. Lorentz and Einstein consider the electron to be a 

 sphere only when at rest and to deform into an ellipsoid of 

 greater and greater eccentricity with increasing velocity 

 until it becomes a disk when the velocity of light is attained. 

 The volume of this ellipsoid is a variable. Bucherer has 

 suggested the same idea of the deformable electron, but in 

 his hypothesis the volume remains constant at all velocities. 



Expressed in similar units, the velocity function of m" in 

 the three cases is as follows : — 



Ab ^- ^HM4r ,og £i-i> 



Lorentz-Einstein . 0>(/3) = (1— £ a )"" l/2 , 



Bucherer <£(£; - (l-^)" 1 / 3 . 



P 2 



