Cathode, Lenard, and Rout gen Rays. 271 



energy are spread into the aether with the velocity of light 

 V, so that when the electron has velocity u the total amount 

 of such electric and magnetic energy is (Searle, Phil. Mag. 

 xliv.) 



e 2 /V. Y + u n \ 



If u is small compared with V this is 



and taking account only of the part of this energy due to 

 motion, we have Heaviside's result : — - 



*V/3KaV 2 or fie 2 u* /3a. 



Now if the process, by which some of our store of energy 

 was converted into electric and magnetic forms on setting 

 the electron in motion, is a reversible one, then on stopping 

 the electron in a suitable manner the electric and magnetic 

 energy ought to flow back to our source or to the stopping 

 body, and if there are no arrangements at the stopping body 

 suitable for storing this as ordinary kinetic or potential 

 energy, it will appear as heat amongst the particles which 

 take part in the stoppage. Thus, then, certain actions of a 

 moving electron take place as if it had a localized inertia, 

 just as in the theory of electric currents a large part of their 

 behaviour is such as it would be if the moving electricity 

 had localized inertia. According to Searle's expression, the 

 inertia or effective mass of the electron becomes a function of 

 its velocity, if we define it as the quantity which is to be multi- 

 plied by half the square of the velocity to give the kinetic 

 energy. With Heaviside's expression for smaller velocities, 

 we should have the inertia equal to 2[ie 2 /3a. But apart from 

 these details, we have only to assume that the energy 

 imparted to an electron when it is set in motion (or the 

 greater part of it) is given up as heat to the material particles 

 which arrest its motion, and is equal to half the square of 

 the velocity multiplied by a certain quantity characteristic 

 of the electron and appearing by the symbol m in the equations 

 of Thomson and Kaufinann. Then the experimental results are 

 at once explained ; for as the negative electrons are the same 

 in all the experiments, m/e has the same value for cathode 

 streams in all gases : the gas facilitates the electric discharge, 

 but does not control it ; as a steam-engine can give the 

 same results with several lubricants, so the cathode stream 

 can give the same stream of electric energy by means of its 



U 2 



