﻿378 Prof. S. C. Kar on the Electrodynamic 



These formulae are exactly similar to the usual formulae 

 for Sx, 8y, Sz, 8t and connect the potentials for any system 

 of axes with those of another moving with velocity v along 

 the axis of x. 



The reversing formulse are 



F = *(F' + v<S>'), G = G', H = H', 

 and ^> = /e /V+^. 



(3) 



Let us suppose an electron moving with velocity v 



along the axis of x and let us take a system of axes moving 



with the electron. It is apparent that for the latter system 



of axes the electron is at rest. The vector potentials 



(F', G', H') = and <!>' = - — , due to a static charge e where 



r' is the distance of the point P at which the potentials are 

 considered. 



For the original system of axes, therefore, we should have 

 according to the formulae of transformation given above, 



F=/™ * , G = 0, H = 0, and <£ = *«,—,. 



t is, however, expressed in terms of the coordinates of the 

 rest system and it will be necessary to transform it to a form 

 involving the coordinates of the original system. 



But if the time-difference between the point P and the 

 electron is A*', then 



r' = cAt' 



- KG \ At 



r vAx~] r\ v Ax~\ 



— K\r = kt 1 . — 



L c J L c r J 



ev 



F = -,G = 0, H = 0, 



and <E> — 



4:TT7 



I" 1 --]' 



which are Lienard's results. 



