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Dealing with the resurgence of 19th-century electromagnetism in physics and electrical engineering, this text describes a series of important experiments, and new technologies based on these experiments, which cannot be explained and analyzed with the modern relativistic electrodynamics of the 20th century. The Newtonian electrodynamics of Coulomb, Ampere, Neumann and Kirchhoff, which was current from 1750 to 1900, is fully reviewed and extended to deal with contemporary research of exploding wires, railguns and other electromagnetic accelerators, jet propulsion in liquid metals, arc plasma explosions, capillary fusion and lightning phenomena. Much of the book is based on the atomic definition of the Amperian current element. Finite element techniques are described for solving many electrodynamic problems.