Electrical Papers (vol. 1)

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Ampère's law/rule/formula called Ampere's "dodge" on p. 261.

It is also interesting, reading Heaviside’s assessment of Ampère’s fundamental law of force (from the quote Alan provided), to remember that he ended up introducing the notion of “impressed forces” in Maxwell field equations (denoting e and h the “impressed electric and magnetic forces at a point,” while he, rather confusingly, called E and H the “electric and magnetic forces of induction”), see Electrical Papers , vol. 1, pp. 428-455. I find this noteworthy since the notion of force itself has subsequently been somewhat confused and reduced to a propagative action (a wave) in field-based E&M theory, consistent with Heaviside’s own dissipative and thermoelectric recasting of Maxwell’s electrodynamics (something, Alan, I mentioned to you and touch upon in a follow up paper appealing to Ampère’s electrodynamic theory from a multiscalar standpoint).

In fact, Heaviside reused the idea that the “activities” of “forces” acting within a dynamic system can be summed up to dU /dt. But he defined that concept of activity as the vector product of a generalized force (e.g. E or H) and a velocity (J or G), meaning the “activity” of the motional electric or magnetic force, see p. 435 (somewhat intuitive, considering it from the perspective of propagating, field-like “forces,” but confusing as well):

“[…] in the dynamical theory, it is the electric current itself that is a velocity, in the generalized sense, with the electromotive force as the generalized force; so that force × velocity = activity.”

For electrical bodies in motion, Heaviside could have taken his cue from Weber’s relative velocity law of inter-actions between elementary charged particles. Symptomatically, he didn’t, his modified (anti-fluidic) energetic conceptualization of electric and magnetic actions and fields—compared to Maxwell’s successively mechanical and quaternionic conceptualizations—betraying his overall view of propagative electromagnetic induction (within which the notion of force, à la Ampère & Weber, gets essentially demoted).

S. Hyacinthi, o.p.n.

Sebastien