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A stringent theory of 1-dimensional alternating electromagnetic fields in solid iron is based on Maxwell's differential equations. Since the permeability is not constant, fundamental problems arise and are discussed. The fields are represented by complex Fourier series, the coefficients of which may be calculated by harmonic analysis of measured static hysteresis loops. A precise method is given to calculate the total power loss due to eddy currents and hysteresis, and close agreement with 50 Hz tests is obtained. A field-penetration function is calculated, and simplified approximate loss formulas are proposed.