chapter  7
54 Pages

Station 4 (1873)

A treatise on electricity and magnetism
ByGiora Hon, Bernard R. Goldstein

Station 4 is the culmination of Maxwell’s methodological odyssey in electromagnetism. Maxwell did not appeal to any new phenomena; from an empirical perspective, there was no motive to revise the theory or to propose a new one. However, from a methodological perspective, there were many novelties to be adopted and applied. Maxwell’s Treatise is a mélange of methodologies and scientific ideas intended for a student of physics as well for a physicist at the cutting-edge of research. Yet, however eclectic the Treatise may appear, it has a systematic methodology. The unifying concepts are energy and lines of force. The emphasis on energy, rather than on force, goes back to the insights of Rankine in the 1850s who noted that energy is the same whether it be mechanical, electrical, magnetic, or chemical. Maxwell modified the methodology of “abstract dynamics” of Thomson and Tait (1867) which they had based on the Lagrangian and the Hamiltonian. For Maxwell such algebraic representations of dynamics were powerful tools that he was happy to apply but, in his view, physics requires more than mere formalism, it must have mental imagery capable of being rendered verbally. Since the analysis in terms of the Lagrangian and the Hamiltonian is purely abstract, being carried out entirely by symbolic operations, Maxwell demanded “retranslation.” He insisted on maintaining the intuitive physical grasp of the phenomena over and above the powerful formalism. He sought to translate formal expressions into mental imagery; indeed, he rendered this requirement a criterion for viable theories.