132 PHYSICS OF THE ELECTRON 



Without any other hypothesis than that of its electric charge, 

 the electron is found to have inertia defined as capacity for kinetic 

 energy, but with a particular law of variation of this as a function of 

 the velocity, and this inertia appears to approach infinity as the 

 velocity approaches that of light. 



The behavior of this law depends very little on the hypothesis 

 made as to the form of the electron and the distribution of the electric 

 charge which it carries. In all cases it is found to be impossible to 

 give the electron a velocity equal to that of light, at least permanently. 



Instead of considering with Max Abraham the electron to be spher- 

 ical at all velocities, Lorentz admits it to be spherical when at rest 

 and to have a uniform distribution of charge; but if all internal forces 

 are solely electromagnetic or act as such, we have the view that the 

 electron is flattened in the direction of motion by a quantity propor- 



/ v\ 



tional to the square of the ratio I /?=. of its velocity to that of 



light, becoming an ellipsoid of revolution, the equatorial diameter 

 remaining equal to that of the original. This leads, as we shall see, to 

 a law of inertia different from that of an invariable sphere. 



We shall likewise see that it does not appear to be necessary to 

 assign to the electrons, the negative ones at least, any other inertia 

 than this in order to account for the dynamic properties of the cathode 

 rays; however, experiments are not yet sufficiently exact to allow us 

 to infer the form of the electron itself, which depends on the law of 

 the variation of the kinetic energy with the velocity. 



(14) Two Problems. We have examined, so far, only the case of 

 an electron in uniform motion in the absence of any external electro- 

 magnetic field capable of modifying the motion of the electron by 

 giving it an acceleration. 



The general problem of the connection between the ether and the 

 electron, which probably represents the most important of the con- 

 nections between ether and matter, is double. 



In the first place, what is the electromagnetic disturbance in the 

 ether accompanying any given motion of the electrons whatsoever? 



In the second place, what motions would free electrons have if dis- 

 placed in an external magnetic field superimposed on that which 

 constitutes their wake? 



(15) The Velocity Wave The Acceleration Wave. We actually 

 possess all the elements necessary for the solution of the first pro- 

 blem, in which the motion is uniform in a particular case. Lorentz 

 has given in a very simple form the general solution by the use of 

 a delayed potential. 



Each element of the charge in motion is determined by its position, 

 its velocity, and its acceleration at the time T, the electric and mag- 

 netic fields at the time T + t, on a sphere having for its centre the 



