him to adapt the mathematics of fluids with continuity, sources, sinks, variable flow, and resistance. It also supplied a basis for representing Faraday's concept of an electro-tonic state characterizing the condition of a conductor in a magnetic field by assigning to any point in space a quantity determinate in magnitude and direction. This eventually became the vector potential. This representation, Maxwell insisted, is not a physical theory.(Maxwell, Papers I, p. 205).
His next electrodynamics paper (1861-1862) introduced the hypothesis of magnetic vortices with idle wheels. Distortions of these vortices were interpreted as a displacement current. This, the crucial step in transforming electrostatics into electrodynamics, supplied a basis for extending Ampère's law to closed circuits. In this paper he also introduced the hypothesis that light consists of transverse undulations of an ethereal medium. His definitive paper, "A Dynamical Theory of the Electromagnetic Field" (1864, Papers, 526-579)14 attempted to put his electrodynamics on a less hypothetical basis in two distinct, but related, ways. First, instead of molecular vortices, he now relied on the general assumption of an ethereal medium filling space, permeating bodies, capable of transmitting motion from one part to another and of communicating that motion to gross matter so as to heat it and affect it in various ways. Maxwell thought this was experimentally established by the work of Faraday, Verdet, and Thomson. (Ibid. p. 528) The second novel feature is a reliance on dynamics, rather than mechanics. Since about 1838 British physicists had been using 'dynamical' for an explanation based on Lagrange's analytic mechanics, rather than on any particular mechanical model. (See Harman, 1982b, pp. 25-27) This entails that the basic explanatory concepts are the mechanical concepts of space, time, force, and energy.15
Though this paper presented formidable difficulties (20 equations in 20 unknowns) it emerged as the definitive paper on electrodynamics. Here, however, we will focus on the problems it presented to Maxwell in Glenlaire. In the Continental tradition Weber had successfully answered Helmholtz's objection that Weber's law violated energy conservation. Ludwig Lorentz derived an electromagnetic theory of light by introducing a retarded potential into distance theory. The two approaches, field theory and distance theory, seemed empirically equivalent. Yet, they had different conceptual foundations. In Maxwell's account displacement was the basic concept. Maxwell was not sure what was displaced, nor even in what direction. In his dynamics paper it pointed in the same direction as the electrical field. His earlier account in terms of distortions of vortices gave the opposite direction. Such uncertainties notwithstanding, if one accepts, as Maxwell did, mechanical explanations as basic and fields as real, then the transmission of force through fields requires that something in the field must move. The most likely source seemed to be polarization of molecules through electromagnetic force. Then positive and negative charges are really phenomenological manifestation of displacement on the bounding surface of a dielectric. Current in wires is a phenomenological manifestation of displacement being absorbed and transformed into heat. As Siegel (1986) put it, Maxwell thought of conductors as leaky condensers. This changes the status of some basic concepts. Thus, the dielectric capacity, 0, and the specific magnetic capacity, 0,
14 The term 'theory' refers to the limited theoretical assumption that variations in the electromagnetic field are causally responsible for the transmission of light and heat. It does not present a theory of what either light or electricity is.
15 Maxwell repeatedly insisted that the concept of energy must be interpreted literally and that mechanical energy be treated as basic.