New techniques for obtaining either a perfectly sinusoidal magnetizing force or flux density in magnetic sheet steel at high flux densities have enabled more reliable performance characteristics to be obtained, which can be extrapolated with greater confidence to still higher densities. The test results for a variety of specimens cover the frequency range 0.2–2.4kc/s, and up to a flux density of 20kG in the case of Permendur (49% cobalt, 49% iron, 2% vanadium), or 16kG for a 0.3% silicon-iron. It is shown that the iron losses for the alternative sinusoidal conditions of magnetization are not very different, except for densities above about 10kG at the lower frequencies. The a.c. permeability decreases appreciably with increase of frequency at medium densities, but at high densities it becomes equal to the d.c. permeability at all frequencies; the higher the frequency, the higher is the density at which the a.c. and d.c. permeability become identical.Further results of practical interest are that thin laminations of high silicon content require to be specially annealed to maintain a lower loss at high densities than thin laminations of low silicon content; flux distortion in the individual laminations substantially increases the loss of a packet of laminations above that obtained when the flux in each lamination is constrained to be sinusoidal; an appreciable error is involved in assuming that test results on a single strip are representative of a packet from the same sheet; the loss exponent of frequency can vary appreciably at saturation densities, but is otherwise virtually constant, whilst the loss exponent of flux density can vary from about 1.6 to 3.