  We present an analysis of the magnetic-field fluctuations in the magnetoionic
medium in front of the radio galaxy 3C 31 derived from rotation-measure (RM)
fits to high-resolution polarization images. We first show that the Faraday
rotation must be due primarily to a foreground medium. We determine the RM
structure functions for different parts of the source and infer that the
simplest form for the power spectrum is a power law with a high-frequency
cutoff. We also present three-dimensional simulations of RM produced by a
tangled magnetic field in the hot plasma surrounding 3C 31, and show that the
observed RM distribution is consistent with a spherical plasma distribution in
which the radio source has produced a cavity.
