﻿76 Dr. W. F, Gr. Swann on tJte Effects of Uniform Motion 



strictly speaking, to be chosen as any corresponding points 

 in the two systems which at some instant in the whole range 

 of time are occupied simultaneously by corresponding elec- 

 trons, and the origin of' time may be taken as any time at 

 which this" occurs. Asa matter of fact, the origin of time 

 does not concern us ; all we are concerned with is difference 

 of time, and we may obviously measure our spacial coor- 

 dinates in the two systems from any corresponding origins 

 we choose, for differences in the choice of the spacial origin 

 only obviously affect the expressions for the above times by 

 a constant. 



The above result is, of course, equivalent to the statement 

 that the condition which must hold is, that if x', if ', z' are 

 the coordinates of any electron in the moving system, 



vx' 



e l;2 \v',y',z' must be the same functions of e _1 < 2 £ — e 1/2 w 2 as 



the x, y, z coordinates in the fixed system are functions of t, 

 and we further see that the values of e l/2 x' } y' , z' for which 

 any state of the aether (due to a certain set of electronic 

 motions) occurs in the system in motion, are the same func- 



vx' 

 tions of e~ l ' 2 t — e [2 .\ 2 as the values of x 3 y, z for the state of 



the aether in the system at rest (due to the corresponding 

 motions there), are functions of t. 



It is interesting to observe that no electromagnetic 

 phenomena have been involved in the deduction of the above 

 facts with regard to the time variable, we have simply used 

 the word " electron " to fix our ideas. The only fundamental 

 thing involved is the idea of the finite time of propagation of 

 an effect from a moving centre of disturbance. 



We must now pass on to consider how the forces due to 

 the electronic motions are modified by the motion of the 

 system as a whole. On page 61) we have written down the 

 forces X, Y, Z on a fixed unit of charge at a point P due to 

 a moving electron a of strength e. If the unit at P is itself 

 moving with velocity p ly q ly r L it constitutes a current in a 

 magnetic field, so that owing to this fact there will be an 

 additional force on it whose components are #17 — ?']/?, 

 r \ 0L ~Piy } P\fi—qi°<.- Thus the total force on our moving- 

 unit will be X 2 , Y 2 , Z 2 , where 



,(X 2 , Y 2 , Z 2 ) = (X + ^i7-n& Y +*-!«— pw, 



Z+pr/3-^a) . . . (8) 



Now let us impart to the whole system a velocity v in the 



direction of the x axis. Let us suppose the electrons to be 



