The paper deals with the eddy currents in thin circular cylinders of uniform conducting material, due to periodic currents in conductors lying parallel to the axis of the cylinder, or to the rotation of the cylinder in a two-dimensional field of force. The first of these problems was discussed by Mr M. B. Field in a paper entitled “Eddy current losses in three-phase cable sheaths,” read before the British Association at their Cambridge meeting in 1904. The solution proposed, however, although probably sufficient for the object, is mathematically defective, in that the field due to the current carried by the cable is assumed as the total field, the effect of the eddy-current field on the eddy currents themselves being left out of account.