312 Models of the Aether. 



many years, attention was directed chiefly to magnetic fields of 

 a steady, or at any rate non-oscillatory, character ; in such fields, 

 the motion of the particles of the medium is continuously 

 progressive ; and it was consequently natural to suppose the 

 medium to be fluid. 



Maxwell himself, as we have seen,* afterwards abandoned 

 this conception in favour of that which represents magnetic 

 phenomena as rotatory. "According to Ampere and all his 

 followers," he wrote in 1870,f " electric currents are regarded 

 as a species of translation, and magnetic force as depending on 

 rotation. I am constrained to agree with this view, because 

 the electric current is associated with electrolysis, and other 

 undoubted instances of translation, while magnetism is asso- 

 ciated with the rotation of the plane of polarization of light." 

 But the other analogy was felt to be too valuable to be 

 altogether discarded, especially when in 1858 Helmholtz 

 extended itj by showing that if magnetic induction is com- 

 pared to fluid velocity, then electric currents correspond to 

 vortex-filaments in the fluid. Two years afterwards Kirchhoff 

 developed it further. If the analogy has any dynamical (as 

 distinguished from a merely kinematical) value, it is evident that 

 the ponderomotive forces between metallic rings carrying electric 

 currents should be similar to the ponderomotive forces between 

 the same rings when they are immersed in an infinite incom- 

 pressible fluid; the motion of the fluid being such that its 

 circulation through the aperture of each ring is proportional to 

 the strength of the electric current in the corresponding ring. 

 In order to decide the question, Kirchhoff attempted, and solved, 

 the hydrodynamical problem of the motion of two thin, rigid 

 rings in an incompressible frictionless fluid, the fluid motion 

 being irrotational ; and found that the forces between the rings 

 are numerically equal to those which the rings would exert on 



* Cf. p. 276. 



t Proc. Lond. Math. Soc. iii (1870), p. 224 ; Maxwell's Sclent. Papers, ii, p. 263. 

 J Cf. p. 274. 



Journnl fur Math. Ixxi (1869) ; Kirchhoff's Ge*amm. AbhandL, p. 404. Cf. 

 also C. Neumann, Leipzig Berichte, xliv (1892), p. 86. 



