﻿deduced from the Electrical Theory of Matter. 83 



motion in the ratio e - 1 ' 2 *^ and it will be unnecessary to 

 repeat the work here. The quantities X -1 . fi~ l , v~ l for this 

 case are, of course, the so-called longitudinal and transverse 

 masses of the electron, first deduced by J. J. Thomson, by 

 Lorentz, and by Abraham, by another method. It is easily 

 seen, from the work in my paper above mentioned, that to 

 tha degree of approximation to which we have restricted 

 ourselves on page 81, the expressions for \, fju, v given by 

 equations (16) are the same as those for the cases pi = v, 

 q l = r l = 0, and these turn out to be 



X = ?? e _3/2 , fj, = w e _1/ ' 2 , v = n e~ lf *, 



where n Q is the acceleration produced by unit force on the 

 electron in the system at rest, which, to the degree of 

 approximation referred to on page 81, is constant, and 

 independent of the direction of the force. 



Suppose now that the component forces on our electron b 

 in the system at rest are functions of x, y, z, and t of the 

 forms 



P = FxO, y,z,t), Q = F,(#, y, z, t\ R = F,(ar, y, z, t), 



then, as we have seen on page 81, the forces P', Q', R' in 

 the moving system are given by 



P' = F^VV, y\ z\ i"), e^Q' = F 2 (eVV, y', z' , t"), 



where t" = e^H-e 1 ' 2 ^ . 



The equations of motion of our electron, in the fixed 

 system, are 



d?x d 2 y \ 



^ = nJFi(tf, y> *> 0» -[$ = ^oF 2 (.r 7 y, z, t), \ 



# T \ • ■ (17) 



and those of the corresponding electron in the moving 



* In considering the force due to an electron at a distance large 

 compared with its dimensions, the shape of the electron is not involved, 

 but in considering the effect of the forces of the field on an electron, the 

 shape is of vital importance, for no matter how small the electron may 

 he, its effective mass depends on its shape, since practically the whole of 

 the electrokinetic momentum associated with it is contained within a 

 region of the same order of magnitude as itself. 



G 2 



