﻿S2 Dr. W. F. Gr. Swarm on ilie Effects of Uniform Motion 



functions of a\ y, z, and t. We may also here remark that, 

 since 



4*rC 2 (/;$r,7i) = (X,Y, Z), 



the results deduced in equation (14) are equivalent to the 

 statement that 



rV'(e-W, + Avvh', 7'- W, e~^f, g>- ^y', V+^ff) | 



are the same functions of 



^V,/, r' and e'^t-^^ 



K15) 



in the moving system, as in the fixed system (a, /3, 7, f, g, h) 

 are functions of #, y, z, and t ; for, as we have above 

 remarked, the results obtained for the vectors due to a single 

 electron may be extended to the total vectors due to all the 

 electrons. The above results are, of course, the same as 

 those obtained by Larmor's transformation. Let us now 

 see whether the modifications of the forces on the electrons, 

 produced by the motion, are such as to maintain them 

 in the state of orbital motion which we have assigned to 

 them. 



The measure of the force acting on the electron in any 

 direction is the rate of increase of the total momentum 

 associated with the electron in that direction. In order to 

 find the accelerations \, fi, v, produced on our electron b by 

 unit component forces in the three coordinate directions, we 

 have to find by how much the velocity must increase in each 

 of those directions, in order that the momentum associated 

 with the motion in the particular direction considered may 

 increase by unity, so that if U, V, W are the component 

 momenta in the three coordinate directions, expressed as 

 functions of the coordinate velocities p ly q l9 r 1? the component 

 accelerations satisfy three equations of the typical form 



1= -— =X S — + /x^ +v^ — . . . . (lb) 

 dt dpi O'/i 0>\ 



The most important case is where the electron is moving 

 parallel to the .raxis with velocity v, so that p x =v 3 q l = r 1 =0. 

 I have, in a former communication *, calculated the values 

 of X, fi, v for this case, assuming, after Lorentz, that the 

 electron, like the matter as a whole, contracts when in 



* Phil. Mag. June 1911, p. 733, also July 1911, p. 223. 



