Electron Theory of Metallic Conduction. 121 



and if we use 



T m = 



we recognize at once the particular form obtained by 

 Lorentz in Jiis treatment of steady electric and thermal 

 currents. 



2. If the acceleration is due to a steady uniform electric 

 field of intensity E superposed on a uniform magnetic field 

 of intensity H, the result is obtained equally readily, but it 

 is necessarily much more complicated. For simplicity it is 

 best to choose one of the coordinate axes, say the x axis, 

 along the direction of the lines of magnetic force ; the 

 equations for the free-path motion of the typical electron, 

 whose velocities at the time t are (f 4 , r) v £,), are then 



If we 



use 



Ah 



"'it 



= eV x , 





dr) t 

 m ^lt : 



= *E,+ 



eK 



c^ 



m ' : 



dt 



= eE z - 



eK 



it is easily verified that the last two equations are equivalent 

 to the following equations : 



'— v - + £) sin ?it+ (— - — 7]) (1 — cos nt), 

 mit J \mn J 



\mn J \mn / v ' 



wherein (f, 97, f) denote the values of (f f , rj t , £) at the 

 instant £ = 0. We conclude, therefore, that the accelerations 

 of the typical electron whose velocity components at the 

 instant t are (f, 7?, f) are, at the time t x , 



in 



Z= ( — - — 7i I n cosn (U—t) — I — - + ?) Jisin w (^ — t). 

 \mn J \mn J 



