In the paper an attempt is made to formulate a theory of the swaying of one span of a single overhead transmission line due to the action of a transverse wind, on the assumption that the “loop” of wire swings as a rigid whole freely suspended at its extremities.The results comprise formulæ for calculating (a) the equilibrium position of the loop in a steady wind, (b) the maximum swing of the loop due to a short gust of known intensity, as well as the rate of decay of the disturbance, and (c) the amount of continuous movement likely to be imparted to the loop by wind gusts of regular periodicity.Diagrams are given to facilitate the estimation of these quantities and a few numerical examples are worked out by way of illustration.Some suggestions for experimental investigation of swaying are made as a consequence of the form of the dynamical equations which occur in the theory.