The magnetic properties of thin mumetal and permalloy “ C ” laminations have been determined with sinusoidal alternating magnetizing forces, and it has been found that for magnetizing forces of the order for which the d.c. permeability is a maximum, the a.c. permeability at, say, 50 cycles per sec. may be less than a tenth of the corresponding value with direct current; whereas for comparatively large magnetizing forces the a.c. and d.c. permeabilities are practically identical.The a.c. flux densities were determined by (a) a mechanical rectifier, (b) a cathode-ray oscillograph, and (c) the Maxwell and the Campbell bridges. Also, by means of the cathode-ray oscillograph, B—H loops were obtained at various frequencies up to 75 cycles per sec. It is shown that these loops become more elliptical as the frequency is increased; but it is pointed out that this is not due to the flux at a given point of the lamination becoming more sinusoidal, but to the average effect of a flux varying enormously in density and in phase over the section of the lamination.The method given in textbooks for calculating the mean flux density in thick iron laminations due to an alternating magnetizing force assumes the permeability to remain constant at a value equal to the maximum d.c. permeability. It is shown in this paper that such a method accounts for only a small fraction of the difference between the densities obtained with alternating and direct current; and it is suggested that a much closer estimate of the a.c. flux density may be made by using the differential permeability derived from the d.c. hysteresis loops instead of the maximum d.c. permeability.A peculiar dissymmetry was observed in the B—H loops obtained with alternating magnetization, this dissymmetry being most marked when the maximum magnetizing force was in the neighbourhood of that corresponding to maximum d.c. permeability. The dissymmetry was perfectly stable but could be reversed by the momentary application of a comparatively large magnetizing force. It could not be reversed by reducing the flux to zero and increasing it again to the original value. No explanation has been found for this phenomenon.The iron loss at 50 cycles per sec. was measured by the Maxwell and the Campbell bridges, and was found to vary approximately as the 1.7th power of the maximum flux density over a very considerable range of the latter.It is shown that although the impedance of an iron-cored choke may be balanced by a resistance and inductance in series in the Maxwell bridge, the flux linkages per ampere and, therefore, the maximum flux density for the same number of turns, may be far smaller for the equivalent inductance than for the actual choke; and the method usually given for calculating the maximum flux density for iron-cored chokes from Maxwell-bridge tests may be in considerable error. It is also shown that values of maximum flux density based upon the equivalent impedance, instead of the equivalent reactance, are in “reasonably close” agreement with those determined with the cathode-ray oscillograph. Further, the values thus calculated from the Maxwell-bridge results are in agreement with those obtained with the Campbell bridge.