Abstract :
L. C. Peterson (communicated after adjournment): In connection with some tests planned to determine the inductive coupling at the higher frequencies between different wires of a system of parallel wires, a theoretical study was made in June and July of 1926, based on a paper by Professor Pleijel entitled “Current and Voltage Relations in a System of Parallel Conductors” and given as reference No. 18 in Mr. Levin´s paper. In his paper, Professor Pleijel gives a set of linear equations connecting the terminal currents and voltages of a multi-wire line. In the underlying transmission theory, the ground is assumed to have infinite conductivity. Mr. Levin states that he has demonstrated the validity of Pleijel´s equations, as regards their form, when the finite conductivity of the ground is taken into account. Such a demonstration is quite unnecessary; indeed, the fact that the equations maintain the same form irrespective of any assumption regarding the ground conductivity, or any approximation introduced in the transmission theory, follows immediately from the general properties of an n-terminal network. The coefficients in Pleijel´s equations (given as eq. (20) in Levin´s paper) uniquely specify the system and hold for all possible terminal connections of the line wares. They offer, therefore, a means of determining the induction in systems of parallel conductors. In a limited number of cases, these coefficients may be calculated from the dimensions of the system. However, calculations being rather laborious, it is advantageous to resort to the experimental determinations of the coefficients.
