A Dynamical Theory of the Electromagnetic Field

"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and deduces that light is an electromagnetic wave.

Following standard procedure for the time, the paper was first read to the Royal Society on 8 December 1864, having been sent by Maxwell to the Society on 27 October. It then underwent peer review, being sent to William Thompson (later Lord Kelvin) on 24 December 1864. It was then sent to George Gabriel Stokes, the Society's Physical Sciences Secretary, on 23 March 1865. It was approved for publication in the Philosophical Transactions of the Royal Society on 15 June 1865, by the Committee of Papers (essentially the Society's governing Council) and sent to the printer the following day (16 June). During this period, Philosophical Transactions was only published as a bound volume once a year, and would have been prepared for the Society's Anniversary day on 30 November (the exact date is not recorded). However, the printer would have prepared and delivered to Maxwell offprints, for the author to distribute as he wished, soon after 16 June.

In part III of the paper, which is entitled "General Equations of the Electromagnetic Field", Maxwell formulated twenty equations which were to become known as Maxwell's equations, until this term became applied instead to a vectorized set of four equations selected in 1884, which had all appeared in "On physical lines of force".

Heaviside's versions of Maxwell's equations are distinct by virtue of the fact that they are written in modern vector notation. They actually only contain one of the original eight—equation "G" (Gauss's Law). Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents (equation "A") with Ampère's circuital law (equation "C"). This amalgamation, which Maxwell himself had actually originally made at equation (112) in "On Physical Lines of Force", is the one that modifies Ampère's Circuital Law to include Maxwell's displacement current.

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