The rise of dimensional analysis in the latter part of the nineteenth century occurred largely in the context of electromagnetism. It soon appeared that the subject, albeit seemingly straightforward, was in fact wrought with difficulties. These revealed deep conceptual issues regarding the character of physical quantities. Usually, whether or not these problems actually constituted inconsistencies was itself a matter of debate. In one instance, however, regarding the electrostatic dimensions of the magnetic pole, all protagonists agreed that the matter required attention. (...) A controversy ensued in 1882. Its resolution partly relied on the realization that it arose from differences between the scientific cultures prevalent on the Continent versus in Great Britain. These cultural differences concerned the possible relevance of the medium in which interactions involving magnetic poles take place, as well as the understanding of permeability in Ampère’s model of magnetism. The controversy around the electrostatic dimensions of the magnetic pole entailed crucial issues that were soon to play just as central a part in a wider debate about the dimensions of electromagnetic quantities in different systems of units. Why the latter topic was never raised during the 1882 controversy provides insights into the early understanding of dimensional analysis. (shrink)

The rise of dimensional analysis in the latter part of the nineteenth century occurred largely in the context of electromagnetism. It soon appeared that the subject, albeit seemingly straightforward, was in fact wrought with difficulties. These revealed deep conceptual issues regarding the character of physical quantities. Usually, whether or not these problems actually constituted inconsistencies was itself a matter of debate. In one instance, however, regarding the electrostatic dimensions of the magnetic pole, all protagonists agreed that the matter required attention. (...) A controversy ensued in 1882. Its resolution partly relied on the realization that it arose from differences between the scientific cultures prevalent on the Continent versus in Great Britain. These cultural differences concerned the possible relevance of the medium in which interactions involving magnetic poles take place, as well as the understanding of permeability in Ampère’s model of magnetism. The controversy around the electrostatic dimensions of the magnetic pole entailed crucial issues that were soon to play just as central a part in a wider debate about the dimensions of electromagnetic quantities in different systems of units. Why the latter topic was never raised during the 1882 controversy provides insights into the early understanding of dimensional analysis. (shrink)

James Clerk Maxwell’s 1865 paper, “A Dynamical Theory of the Electromagnetic Field,” is usually remembered as replacing the mechanical model that underpins his 1862 publication with abstract mathematics. Up to this point historians have considered Maxwell’s usage of Lagrangian dynamics as the sole important feature that guides Maxwell’s analysis of electromagnetic phenomena in his 1865 publication. This paper offers an account of the often ignored mechanical analogy that Maxwell used to guide him and his readers in the construction of his (...) new electromagnetic equations. The mechanical system consists of a weighted flywheel geared into two independently driven crank wheels in what amounts to a mechanical differential. I will demonstrate how Maxwell made use of the analogy between his flywheel system and electromagnetic induction to ground his study of electromagnetism in clear mechanical conceptions and to structure the derivation of the equations that together are now recognized as Maxwell’s equations for electrodynamics. By reconceiving specific components of his model in electromagnetic terms, while at the same time retaining many of the relations between concepts in the mechanical case, Maxwell gradually assembled increasingly generalized equations for electromotive force. Maxwell thus realized a much sought after balance between physical analogy and abstract mathematics in this, the last of his three seminal papers on electromagnetism. (shrink)