In the course of an extended series of investigations into the relations of magnetism and stress, part of which is already published in the Transactions (vol. xxxv.), I was led to consider the effect of a current passing along a wire upon its longitudinal magnetic intensity. Wiedermann, Buff, and Villari have discussed this problem in some of its aspects. It does not seem possible, however, to deduce from their results completely satisfactory conclusions as to the effect of the current upon the apparent longitudinal permeability. The question, as it presented itself to my mind, was not so much as to the effect of a varying current along the wire upon the apparent longitudinal moment, but rather as to the behaviour of the wire in various longitudinal fields according as it was carrying a current or not.