On the theoretical basis of Carson´s equations

In 1926 Carson produced his paper on ground return effects for overhead wires. It is surmised that the intended application of this work was telegraph circuits. The equations, however, have since been applied to transmission networks ranging from printed circuit boards to power systems. Carson in his derivation makes many assumptions, most of which are only alluded to. This makes defining the boundary conditions and consequently the scope of applicability for the work difficult. The basis for his work was an integral wave equation of general form, the derivation of which can be traced through later papers on the subject to a paper by Von Hoerschelmann. Efforts to obtain copy of Von Hoerschelmann´s paper have made it apparent that this derivation is not available. This paper re-derives the wave equation of general form, details the assumptions used in derivation, compares them to what are believed to be Carson´s assumptions and so defining the scope of Carson´s equations.