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The paper consists of three parts, I??Induced Potentials, II??Direct Hits, and III??Other Effects. The work of previous investigators is briefly reviewed, and the limitations of their premises pointed out. Under Part I a generalized theory of ideal ground wires is offered, which takes into account the law of cloud discharge, the distribution of bound charge, and the formation of traveling waves. It is found that the protective ratio is independent of these factors. A more extensive theory taking the additional factors of successive reflections and tower resistance into account is then developed. Part II discusses the probability of a line's being hit, and applies a method for computing the effect of successive reflections to the calculation of potentials on the line and ground wires. Curves of these potentials at successive towers, and as functions of tower resistances and of time, are given. Part III discusses the effect of ground wires on attenuation, telephone interference, zero phase sequence reactance, corona, and the reduction in surge impedance due to the introduction of extra ground wires. There are three mathematical appendixes. In Appendix I, Maxwell's electrostatic and electromagnetic coeficients are reviewed, and the theory of traveling waves on any number of parallel wires is developed, including the behavior of these waves at rather general transition points. While this extension to the theory of traveling waves was developed incidental to the study of ground wire theory, it is believed to be of considerable interest and value on its own account.