INTERACTIONS OF MOVING ELECTRONS 213 



the mechanical problems of falling bodies, railroad 

 trains, aeroplanes, the transmission of sound, or even 

 molecular motions in gases and liquids, we may con- 

 sider mass to be invariable. For such velocities as 

 we meet hi the transmission of electricity through 

 metallic or electrolytic conductors the mass of the 

 electron is invariable except as it may be influenced by 

 the presence of other moving electrons. In the case 

 of electrons emitted by radioactive substances we can- 

 not consider the mass invariable, for it will depend 

 upon its velocity. 



As to the variation hi apparent mass and hence in 

 kinetic energy due to the motions of other electrons, 

 we may say that it always requires more energy to 

 impart a given velocity to an electron if it is set into 

 motion parallel with that of another electron, but less 

 energy if its direction of motion is parallel and opposite 

 to that of another electron. 



In establishing a current, say i, in a conductor of 

 more than one turn, e.g. in a solenoid, the mass of each 

 electron is dependent upon the existing motion of all 

 the other electrons not only hi its own loop but also 

 in all the other loops. The calculation of the increase 

 in mass of the electron under consideration is therefore 

 rendered too difficult except hi the case of a few cir- 

 cuits of simple geometrical form. The energy re- 

 quired to establish i depends upon the mass and this 

 in turn upon the configuration of the circuit and upon 

 the current. For each electron the energy will be 

 one half the product of its mass and the square of its 

 velocity. In a circuit like that of a metallic conductor, 

 where the number of free electrons available for transfer 



