In this paper a discussion of the mode of description of the linear paths in the (log b, n) diagram—described in previous papers—was given. It was shown that the assumption that fatigue was induced by oscillation of a wire enabled one, in almost all cases, to predict accurately the mode of description of these paths. In a few cases, however, when the condition of the wire was such that the critical angle fell within the range of experimentally observed angles of oscillation, the mode of description of the linear paths agreed with the supposition that oscillation diminished fatigue. The truth of this supposition seemed also to be confirmed by the observed rate of decrease of oscillations in these cases; but further experimental evidence is required to fully test the point.