Melsom and Booth have investigated experimentally the theory of overlapping joints, dividing the resistance of the joint into two parts: one representing the resistance due to the contact, and the other that due to the stream lines of the current at the joint. In the present paper the latter part is obtained theoretically in terms of elliptic functions. The result is expanded and leads to a very simple formula, with which the experimental results of Melsom and Booth are found to agree.