﻿70 Dr. W. F. G. Swami on the Effects of Uniform Motion 



The whole field at the point P may be looked upon as 

 being made up o£ the parts contributed by the individual 

 electrons, the effect contributed by each electron depending 

 on the position, and motion, suffered by that electron at a 

 time St earlier than t, where St is a quantity varying for each 

 electron, being in fact the time taken for light to travel from 

 the point occupied by the electron at the time t — St to the 

 point P. Thus to each instantaneous state of the aether at P, 

 there corresponds a set of instantaneous electronic distri- 

 butions and motions, which have occurred at varying times 

 earlier than t, and which have been responsible for the state 

 of affairs at P. We shall speak of these instantaneous 

 motions as giving rise to a simultaneous set of forces at P, 

 including of course in our meaning the whole field produced 

 by the electrons, and not merely the part due to the motions 

 alone. 



Now in order to study the effect of uniform translatory 

 motion on the force at P', the point in the moving system 

 which corresponds to the point P in the fixed system *, we 

 shall first find the condition, that if a certain set of instan- 

 taneous electronic motions give rise to a simultaneous set of 

 forces at the point P in the fixed system, the corresponding- 

 set of instantaneous motions shall give rise to a simultaneous 

 set of forces at the point P' in the moving system. 



Consider two corresponding orbits of some electron in the 

 fixed and moving systems respectively. Suppose that the 

 time taken by the electron in the moving system to describe 

 its orbit is k times the time taken by the electron in the fixed 

 system, where k is a quantity as yet undetermined. In virtue 

 of , the different rates of description of the orbits, we shall 

 periodically have our two electrons occupying corresponding 

 points in their orbits at the same time, and as a matter of 

 fact, choosing any point in the orbit in the system at rest, 

 we can always find some time sufficiently remote at which 

 the electron in the fixed system occupied the point and 

 simultaneously the corresponding electron occupied the 

 point 0', which is the point in the moving system corre- 

 sponding to Of. It will simplify matters if we take this 

 remote instant as our origin of time. Now suppose that the 

 instantaneous motion of our electron at the point produces 



* P' is the point to which P moves when the whole system S t is shrunk 

 in the x direction in the ratio e -1 /-. It is in this sense that the word 

 " Corresponding " is used. 



t At. least we can always find a time at which one electron occupied 



the point and the other occupied a point which is as near to 0' as we 

 _i 



lease. 



