340 The Followers of Maxwell. 



the location of the charge must produce a continuous alteration 

 of the electric field at any point in the surrounding medium ; or, 

 in the language of Maxwell's theory, there must be displacement- 

 currents in the medium. It was to these displacement-currents 

 that Thomson, in his original investigation, attributed the 

 magnetic effects of moving charges. The particular system 

 which he considered was that formed by a charged spherical 

 conductor, moving uniformly in a straight line. It was assumed 

 that the distribution of electricity remains uniform over the 

 surface during the motion, and that the electric field in any 

 position of the sphere is the same as if the sphere were at 

 rest ; these assumptions are true so long as quantities of order 

 (V/c) 2 are neglected, where v denotes the velocity of the sphere 

 and c the velocity of light. 



Thomson's method was to determine the displacement- 

 currents in the space outside the sphere from the known 

 values of the electric field, and then to calculate the vector- 

 potential due to these displacement-currents by means of the 

 formula 



where S' denotes the displacement-current at (x'y'z f ). The 

 magnetic field was then determined by the equation 



H = curl A. 



A defect in this investigation was pointed out by Fitz Gerald, 

 who, in a short but most valuable note,* published a few months 

 afterwards, observed that the displacement-currents of Thomson 

 do not satisfy the circuital condition. This is most simply seen 

 by considering the case in which the system consists of two 

 parallel plates forming a condenser; if one of the plates is 

 fixed, and the other plate is moved towards it, the electric field 

 is annihilated in the space over which the moving plate travels : 

 this destruction of electric displacement constitutes a displace- 

 ment-current, which, considered alone, is evidently not a closed 



* Proc. Roy. Dublin Soc., November, 1881 ; Fitz Gerald's Scientific Writings, 

 p. 102. 



