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It has recently been discovered that it is possible to reduce skin effect losses in transmission Iines by properly laminating the conductors and adjusting the velocity of transmission of the waves. The theory for such laminated transmission lines is presented in the case of planar systems for both infinitesimally thin laminae and laminae of finite thickness. A transmission line completely filled with lamimated material is discussed. An analysis is given of the modes of transmission in a laminated line, and of the problem of terminating such a line.