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 decide between the theories of W. Weber, F. E. Neumann, Riemann, and Clausius, who had attempted to explain electrodynamic phenomena by the assumption of forces acting at a distance between two portions of the hypothetical electrical fluid,—the intensity being dependent not only on the distance, but also on the velocity and acceleration,—and the theory of Faraday and Maxwell, which discarded action at a distance and assumed stresses and strains in the dielectric. His experiments favoured the British theory. He wrote on abnormal dispersion, and created analogies between electro-dynamics and hydrodynamics. Lord Rayleigh compared electro-magnetic problems with their mechanical analogues, gave a dynamical theory of diffraction, and applied Laplace's coefficients to the theory of radiation. Rowland made some emendations on Stokes' paper on diffraction and considered the propagation of an arbitrary electro-magnetic disturbance and spherical waves of light. Electro-magnetic induction has been investigated mathematically by Oliver Heaviside, and he showed that in a cable it is an actual benefit. Heaviside and Poynting have reached remarkable mathematical results in their interpretation and development of Maxwell's theory. Most of Heaviside's papers have been published since 1882; they cover a wide field.

One part of the theory of capillary attraction, left defective by Laplace, namely, the action of a solid upon a liquid, and the mutual action between two liquids, was made dynamically perfect by Gauss. He stated the rule for angles of contact between liquids and solids. A similar rule for liquids was established by Ernst Franz Neumann. Chief among recent workers on the mathematical theory of capillarity are Lord Rayleigh and E. Mathieu.

The great principle of the conservation of energy was established by Robert Mayer (1814–1878), a physician in Heilbronn, and again independently by Colding of