Before the classical researches of Hertz in 1886 and 1887, many observers had noticed curious effects due to electric sparks produced at a distance which were commonly ascribed to ordinary electrostatic or electro-magnetic induction.
Moreover, his association with glass manufacture led him to study the refractive indices of different kinds of glass; he further undertook abstruse researches on electrostatic capacity, the phenomena of the residual charge, and other problems arising out of Clerk Maxwell's electro-magnetic theory.
The case of electro-magnetic forces between two conductors carrying electric currents affords an example of a statement of motion in terms of force of a highly artificial kind.
This first success of Faraday in electro-magnetic research became the occasion of the most painful, though unfounded, imputations against his honour.
In 1883 he went to Kiel, becoming Privatdozent, and there he began the studies in Maxwell's electro-magnetic theory which a few years later resulted in the discoveries that rendered his name famous.
The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring.