This investigation deals with the shielding which exists within hollow iron cylinders when placed in a uniform transverse magnetic field. This transverse field divided by the internal magnetic field is defined as the shielding ratio. For the thin iron cylinders experimented with, it appears from various mathematical contributions to the subject that the shielding ratio minus unity may for present purposes be taken to be proportional to certain geometrical data and to the permeability (the permeability being large). By means of a rotating inductor within the shield, connected with a ballistic galvanometer, experimental determinations of the shielding ratio are made under various conditions of magnetisation; and an endeavour is also made to show how far and under what conditions these results approximate to theoretical formulas which assume the permeability to be uniform all round the shield, and the absence of retentivity and coercive force in the iron. Two iron shields were experimented with, the hysteretic constants (η) being ·0015 and ·0028 respectively.