On the theory of Kirchhoff's method for the determination of electrical conductivity

A measure of unification is achieved for the purpose of analyzing the steady current flows through elongated cylinders of general section which are activated by a pair of small electrodes on the end faces and are relevant to a scheme of Kirchhoff for determining the electrical conductivity of homogeneous materials; and this features, in a central role, the harmonic Green's function which satisfies a Neumann condition on the boundary of an infinitely long duct whose section duplicates that of the appropriate cylinder. The utility of a Green's function formalism is brought out with specific numerical details in the respective cases of circular and square cross-sections.