﻿FitzGerald Lorentz Contraction. 8 ( J 



v 

 systems follows to any order of -^ , the restriction to the 



second order involved in 'iEtber and Matter' being now 

 generally known to be unnecessary. Corresponding singu- 

 larities in the two systems are shown to be of the same 

 Strengths, and it is concluded that the system S t represents 

 what S becomes when set in motion ; the theorem thus 

 indicates a contraction of the system in the ratio e -12 to unity. 



The present paper forms an inquiry as to how far the above 

 conclusion is justified, and in fact, as to how far the electro- 

 magnetic equations, by themselves, do form a sufficient basis 

 for the explanation of all the phenomena concerned. The 

 points involved are perhaps best introduced by considering 

 one or two actual examples. 



We first remark that a solution of the electromagnetic 

 equations, giving the field at any point P and time t, duo to a 

 point electron moving in any manner can be obtained, as is 

 well known, in terms of two potentials of the form, 



A- c* A - «[T 1__. 



[*-$)]• "[<-$)]' 



where r is the distance of the point P, not from the position 

 of the electron at the time t, but from some other point 0' 

 previously occupied by the electron, and so situated that the 

 time taken by the electron to go from 0' to is the same as 

 the time taken by light to travel from 0' to P. V is a vector 

 representing the velocity of the electron when at 0', and V r 

 is the component of V resolved along O'P. The vectors F 

 and H, representing the setherial displacement and magnetic 

 vectors respectively, are related to the scalar and vector 

 potentials cf> and A by the equations 



F=— A— grad<£, H = rotA. 



Now suppose we have a single electron, alone in empty space, 

 describing a closed orbit s } . We may say that tins is im- 

 possible without a distribution of electrons of opposite sign 

 inside the orbit ; there is no doubt, however, that algebraical 

 functions of as, y, z, and t exist, satisfying the electromagnetic 

 equations, and corresponding to this single electron, lor no 

 matter how the electron may be supposed to move, we can, 

 theoretically, at each instant write down the values of </> and 

 A corresponding to the case, the difficulties involved in so 

 doing being merely algebraical. The values of the authorial 

 displacement and magnetic vectors obtained in this way 



* Sec ' Theory of Electrons,' by Lorentz, p. 50, 



