This paper has for object the calculation of a ladder network, using trigonometrical functions of real multiples of (– I)¼ which, in many cases, simplify practical formulae. The work was prepared particularly for application to transmission lines, conductors in electrical machines, and isolated cylindrical conductors. The effect of the conjunction of two or more dissimilar networks is considered, leading to a method of assessing the impedance of a conductor of any shape embedded in an open slot cut in highly permeable material.