Maxwell's Mathematical Rhetoric - Rethinking the Treatise on Electricity and Magnetism

This literary reading reveals that Maxwell himself wrote with an expressed interest in questions of rhetoric - particularly of mathematical rhetoric.  Maxwell writes with an evident intent to shape new mathematical forms, designed to lead the reader to new conceptual approaches to the natural world.  What results is a strong reaffirmation in practice of the concept of natural philosophy, as distinct from merely technical scientific advance.  This yields a number of important features.

First among them must be Maxwell's dramatic turn to the Lagrangian form in which to present the concept of the electromagnetic field and, in the same mode, to reveal the electromagnetic theory of light.  Narrow readings of the Treatise have regarded this as a mere matter of convenience, or even whim, on Maxwell's part.  Lagrange's equations appear in the Treatise as the culmination of a long series of rhetorical moves, including (among others) Green's theorem, Gauss's potential theory, and Faraday's lines of force - all of which have prepared the reader for the Lagrangian vision of a natural world that is whole and connected:  a veritable sea-change from Newton's vision.