Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/330



early attempts of Thomson and Maxwell to represent the electric medium by mechanical models opened up a new field of research, to which investigators were attracted as much by its intrinsic fascination as by the importance of the services which it promised to render to electric theory.

Of the models to which reference has already been made, some—such as those described in Thomson's memoir of 1847 and Maxwell's memoir of 1861-2—attribute a linear character to electric force and electric current, and a rotatory character to magnetism; others—such as that devised by Maxwell in 1855 and afterwards amplified by Helmholtz —regard magnetic force as a linear and electric current as a rotatory phenomenon. This distinction furnishes a natural classification of models into two principal groups.

Even within the limits of the former group diversity has already become apparent; for in Maxwell's analogy of 1861-2, a continuous vortical motion is supposed to be in progress about the lines of magnetic induction; whereas in Thomson's analogy the vector-potential was likened to the displacement in an elastic solid, so that the magnetic induction at any point would be represented by the twist of an element of volume of the solid from its equilibrium position; or, in symbols,

where a denotes the vector-potential, E the electric force, B the magnetic induction, and e the elastic displacement.

Thomson's original memoir concluded with a notice of his intention to resume the discussion in another communication His purpose was fulfilled only in 1890, when he showed tha