But in the transition from molecular theory to the electrodynamics of extended media, all magnetism has to be replaced by a distribution of current; the latter being now specified by volume as well as by flow so that (u,v,w) ST is the current in the element of volume 6T.
Another powerful reason for taking the aether to be stationary is afforded by the character of the equations of electrodynamics; they are all of linear type, and superposition of effects is possible.
Neither of these men professed to employ the calculus itself, but they recognized fully the extraordinary clearness of insight which is gained even by merely translating the unwieldy Cartesian expressions met with in hydrokinetics and in electrodynamics into the pregnant language of quaternions.
He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established mathematically the laws of the induction of electric currents.
It is on the service that he rendered to science in establishing the relations between electricity and magnetism, and in developing the science of electromagnetism, or, as he called it, electrodynamics, that Ampere's fame mainly rests.