This article examines the gradual development of James Clerk Maxwell’s electromagnetic theory, arguing that he aimed at general structures through his models, illustrations, formal analogies, and scientific metaphors. It also considers a few texts in which Maxwell expounds his conception of physical theories and their relation to mathematics. Following a discussion of Maxwell’s extension of an analogy invented by William Thomson in 1842, the article analyzes Maxwell’s geometrical expression of Michael Faraday’s notion of lines of force. It then revisits Maxwell’s honeycomb model that he used to obtain his system of equations and the concomitant unification of electricity, magnetism, and optics. It also explores Maxwell’s view about the Lagrangian form of the fundamental equations of a physical theory. It shows that Maxwell was guided by general structural requirements that were inspired by partial and temporary models; these requirements were systematically detailed in Maxwell’s 1873 Treatise on electricity and magnetism.
Fundamental System of Equations for Electromagnetic Field Momentum and Energy in an Inhomogeneous Medium. II. Fundamental Equations in Cartesian Basis
