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A simple modification of the jig proposed by the IUCr Commission on Crystallographic Apparatus for the measurement of polarization ratios for X-rays allowing the full rotation of the detector arm permits cancellation of the first-order errors by averaging pairs of measurements differing by 180° around the rotation axis of the detector arm. The plot of Imeas as a function of cos2 Φ, where Φ is the angle between the detector arm and one of the principal directions of polarization in the beam gives a reliable value of the polarization ratio K. The experimental results are: Mo Kα 0.969 ± 3, 0.970 ± 3; Cu Kα 0.908 ± 5, 0.897 ± 5 for a 0.42° and a 0.60° FWHM graphite monochromator respectively.