186 L. Page — Relativity and the Ether. 



Hence the resultant force F 2 on the electron due to its own 

 field is 





6-rrC a 



If <|> is the acceleration of that plane perpendicular to the Z 

 axis which cuts the electron into two parts having equal 

 charges, 



+ = <mA + ^ 



Hence 



F * = - SS3* ( 28 ) 



justifying the assumption made in discussing the effects of 

 ether on matter. The "Kuhmasse" m is found to be a 

 function only of the charge e and radius a of the electron ; 



(29) 



Qirc'^a 



which is exactly the same expression as that for the mass of 

 the quasi-stationary Lorentz electron. However it is to be 

 noted that the force on the electron due to its own field is not 

 the product of the mass of the electron by the acceleration of 

 its geometrical center, but the product of the mass by the 

 acceleration of that plane, perpendicular to the direction of 

 acceleration, which cuts the electron into two parts having 

 equal charges. 



It can easily be shown that when the electron is in motion 

 relative to iTthe tubes of strain will be circles with the same 

 centers but larger radii. If i denotes the time measured from 

 the instant when the electron is at rest in K, either earlier or 

 later, the radius of that tube of strain defined by the parameter 



/ c 4 

 h in (26) will be \/ A 2 + \. C V . If t is earlier than the in- 



stant when the electron is at rest in K, the field will be limited 



by the plane z = ct — ; if later, by the plane z = — ct — -r 



According to (16) both the apparent force on the electron due 

 to the outside field, and the retarding force due to the elec- 

 tron's own field, will remain constant. The acceleration f at 

 any time will be given by (18), where c/3 is the velocity 

 at the instant considered of that plane, perpendicular to 



