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Arguably the most influential nineteenth-century scientist for twentieth-century physics, James Clerk Maxwell (1831–1879) demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field. A fellow of Trinity College Cambridge, Maxwell became, in 1871, the first Cavendish Professor of Physics at Cambridge. His famous equations - a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density - first appeared in fully developed form in his 1873 Treatise on Electricity and Magnetism. This two-volume textbook brought together all the experimental and theoretical advances in the field of electricity and magnetism known at the time, and provided a methodical and graduated introduction to electromagnetism. Volume 1 covers the first elements of Maxwell's electromagnetic theory: electrostatics, and electrokinematics, including detailed analyses of electrolysis, conduction in three dimensions, and conduction through heterogeneous media.

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Theories of the constitution of bodies suppose them either to be continuous and homogeneous, or to be composed of a finite number of distinct particles or molecules. In certain applications of mathematics to physical questions, it is convenient to suppose bodies homogeneous in order to make the quantity of matter in each differential element a function of the coordinates, but I am not aware that any theory of this kind has been proposed to account for the different properties of bodies. Indeed the pro­perties of a body supposed to be a uniform plenum may be affirmed dogmatically, but cannot be explained mathematically.