[From the Proceeding of the Royal Society, No. 132, 1872.] 



XLIX. On the Induction of Elect Currents in an Infinite Plane Slifct of 



Uniform Conductivity. 



1. WHEN, on account of the motion or the change of strength of any 

 magnet or electro-magnet, a change takes place in the magnetic field, electro- 

 motive forces are called into play, and, if the material in which they act is a 

 conductor, electric currents are produced. This is the phenomenon of the induc- 

 tion of electric currents, discovered by Faraday. 



I propose to investigate the case in which the conducting substance is in 

 the form of a thin stratum or sheet, bounded by parallel planes, and of indefi- 

 nite extent. A system of magnets or electro-magnets is supposed to exist on 

 the positive side of this sheet, and to vary in any way by changing its position 

 or its intensity. We have to determine the nature of the currents induced in 

 the sheet, and their magnetic efiect at any point, and, in particular, their 

 reaction on the electro-magnetic system which gave rise to them. The induced 

 currents are due, partly to the direct action of the external system, and partly 

 to their mutual inductive action ; so that the problem appears, at first sight, 

 somewhat difficult. 



2. The result of the investigation, however, may be presented in a re- 

 markably simple form, by the aid of the principle of images which was first 

 applied to problems in electricity and hydrokinetics by Sir W. Thomson. The 

 essential part of this principle is, that we conceive the state of things on the 

 positive side of a certain closed or infinite surface (which is really caused by 

 actions having their seat on that surface) to be due to an imaginary system on 

 the negative side of the surface, which, if it existed, and if the action of the 



