﻿68 Dr. W. F. G. Swarm on the Effects of Uniform Motion 



In what follows we shall look upon a piece of matter as 

 simply a system of electrons in motion, and though we shall 

 for convenience rise the term " orbital motion," it will be 

 seen that what is said is not restricted to the case where the 

 electrons stay approximately in one place, and revolve round 

 and near to fixed centres ; it will apply even to cases where 

 the electrons describe paths in which they wander from 

 molecule to molecule. It is not even necessary to restrict 

 our work to systems in equilibrium : indeed, the equilibrium 

 of all electronic motions in a piece of matter is probably of a 

 secular or possibly semi-statistical nature, there is at any 

 rate always disintegration at the surface. 



We shall then imagine a system of electrons S l5 at rest as 

 a whole, but having motions relative to one another which 

 are consistent with the laws of electrodynamics. We shall 

 then fix our attention on a corresponding system S 2 , moving 

 in the direction of the axis of x with velocity v, and with 

 the orbits of all its electrons shrunk in the direction of the 

 axis of x in the ratio e -1 ' 2 ; we shall inquire whether 

 movement of the electrons of S 2 can, consistently with the 

 laws of electrodynamics, take place in these orbits, and if 

 such motions are possible, we shall inquire how the nature of 

 the motion in these orbits must be modified in order to make 

 them possible. We shall find that such a type of motion is 

 possible, and the necessary adjustment of the rates of motion 

 in the orbits will bring out the real physical significance 

 of the peculiar time variable occurring in Larmor's trans- 

 formation. 



First, with regard to the field produced by a moving 

 electron. A moving mass of electricity, of volume density 

 p, produces on unit charge at rest at a point P a force, each 

 of whose components X, Y, Z consists of two parts, a part 

 derivable from a potential yfr, and a part X 1; Y l5 Z,, arising 

 out of the changing magnetic field at the point P. The 

 potential yjr is of the form 



* = c ! J~M</s 



where d$ is an element of volume, and the square bracket is 

 meant to indicate that in considering the contribution of the 

 element dS at the time t, we must not put in the value of p 

 then existing in it, but the value which existed there at the 



time t — j\, where r is the distance from the element to the 



point P. The components a, /3, y of the magnetic field may 



