﻿Fit.: Gerald Lorentz Contraction. 9)> 



initial state of the field and of the oscillations on the spheres, 

 which of course depend on the manner in which they were 

 originally brought into the vicinity of each other. 



lieturning now to the problem of uniform translation, we 

 see that we are not justified in saying that the solution 

 suggested by the transformation is one which could possibly 

 have arisen out of the system S. The transformation simply 

 tells us that if S satisfies the electromagnetic scheme, Si also 

 satisfies it, but so would a system of electrons moving in 

 orbits of similar shapes to those of S x but all slightly or in 

 fact completely separated out, instead of being pushed 

 together, for the total solution in any configuration of the 

 system is simply the sum of the solutions which we should 

 obtain by considering each electron as moving independently 

 in its orbit, and we can put the orbits wherever we please, 

 and by adding the independent solutions obtain a solution of 

 the electromagnetic equations. We may even, if we wish, 

 imagine the orbits altered in shape. In fact, it seems that 

 the transformation, by itself, tells us astonishingly little ; it 

 simply tells us that if one solution of (1) exists, it is possible 

 to find another corresponding to the same electrons, but then 

 we can theoretically write clown the solution corresponding 

 to the electrons moving in any orbits and in any manner we 

 choose to assign, and the solution given by the transformation 

 possesses no unique advantage in that it reduces to the solution 

 for the system at rest when we put v equal to zero, for we 

 can imagine any number of types of electronic motion, only 

 differing from, the motions in the system at rest by functions of 

 the velocity v, which vanish ichen v is put equal to zero, and we 

 can always, as we have seen, find the field consistent with 

 these motions. Even considering a molecule in the system 

 at rest ; though the field in that molecule certainly is con- 

 sistent with the electromagnetic scheme, we can realize how 

 far this is from being the sole factor in the determination of 

 the electronic motions, and how large a partis played by what 

 we have termed the subsidiary laws, when we observe that 

 as far as compliance with the electromagnetic scheme is con- 

 cerned, the electrons in the molecule might move in any paths 

 we choose to assign. 



The objection here raised against the solution given bv the 

 transformation is on a different plane to objections which 

 might at first sight be raised against the solutions of many 

 dynamical problems, in which the final solutionis obtained so 

 as to satisfy certain conditions without inquiry as to the mode 

 of transition from one state to the other, for in those problems 

 the conditions are usually such as to completely restrict the 

 final solution to one. and only one dorm. In dealing with 



