Models of the Aether. 3 13 



each other if they were traversed by electric currents pro- 

 portional to the circulations. 



There is, however, an important difference between the two 

 cases, which was subsequently discussed by W. Thomson, who 

 pursued the analogy in several memoirs.* In order to represent 

 the magnetic field by a conservative dynamical system, we shall 

 suppose that it is produced by a number of rings of perfectly 

 conducting material, in which electric currents are circulating ; 

 the surrounding medium being free aether. Now any perfectly 

 conducting body acts as an impenetrable barrier to lines of 

 magnetic force ; for, as Maxwell showed,f when a perfect con- 

 ductor is placed in a magnetic field, electric currents are induced 

 on its surface in such a way as to make the total magnetic force 

 zero throughout the interior of the conductor.^ Lines of force 

 are thus deflected by the body in the same way as the lines of 

 flow of an incompressible fluid would be deflected by an obstacle 

 of the same form, or as the lines of flow of electric current in a 

 uniform conducting mass would be deflected by the introduction 

 of a body of this form and of infinite resistance. If, then, for 

 simplicity we consider two perfectly conducting rings carrying 

 currents, those lines of force which are initially linked with a 

 ring cannot escape from their entanglement, and new lines 

 cannot become involved in it. This implies that the total 

 number of lines of magnetic force which pass through the 

 aperture of each ring is invariable. If the coefficients of self 

 and mutual induction of the rings are denoted by Z,, Z 2 , Z 12 , 

 the electrokinetic energy of the system may be represented by 



T = J (Z,*V + 2Z 12 ^ + Z 2 v), 



where i\, i> denote the strengths of the currents; and the 

 condition that the number of lines of force linked with each 

 circuit is to be invariable gives the equations 

 Liii + Z 12 i 2 = constant, 

 L z iz = constant. 



* Thomson's Reprint of Papers in Elect, and Mag., 573, 733, 751 (1870- 

 1872). t Maxwell's Treatise on Elect, and Mag., 654. 



% For this reason "W. Thomson called a perfect conductor nn ideal extreme 

 diamagnetic. 



