Use of the tangent chart for solving transmission line problems

THE general problem of finding the steady-state electrical conditions at some point of a transmission line when they are known at some other point has been a fascinating one for writers, and many schemes, most of them giving approximate solutions, have been proposed for lessening the labor of solving such problems. Dr. A. E. Kennelly has shown that the exact solution of such problems is most simply given by the use of hyperbolic functions and he has been a pioneer in the application of these functions to transmission line problems. About five years ago the writer devised a method, based on hyperbolic functions, for obtaining the exact solution, by applying them in such a manner that the use of tables is unnecessary, provided a special diagram, called a tangent chart, is available. The chart is entirely general in its application, not depending on any particular frequency or length of line. It was described in an article in French, prepared by Messrs. Marius Latour and Geo. Viard from notes furnished them by Dr. C. O. Mailloux, which was published in La Revue Générale de l'Electricité, July 20, 1918. The very favorable consideration which the method received in Europe, and the demand for the publication of a description of the method in the English language, led the writer to take up its study anew, recently, with the idea of improving it, and extending its applicability and practical usefulness. The result is the present paper, which contains an entirely new presentation of the method, in its latest and most complete form.