  We present high-quality VLA images of the FR I radio galaxy 3C 31 in the
frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40
arcsec. Our new images reveal complex, well resolved filamentary substructure
in the radio jets and tails. We also use these images to explore the spectral
structure of 3C 31 on large and small scales. We infer the apparent magnetic
field structure by correcting for Faraday rotation. Some of the intensity
substructure in the jets is clearly related to structure in their apparent
magnetic field: there are arcs of emission where the degree of linear
polarization increases, with the apparent magnetic field parallel to the ridges
of the arcs. The spectral indices are significantly steeper (0.62) within 7
arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra
of the jet edges are also slightly flatter than the average for their
surroundings. At larger distances, the jets are clearly delimited from
surrounding larger-scale emission both by their flatter radio spectra and by
sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of
3C 31's jets is very close to that found in other FR I galaxies where their
jets first brighten in the radio and where X-ray synchrotron emission is most
prominent. Farther from the nucleus, where the spectra flatten, X-ray emission
is fainter relative to the radio. The brightest X-ray emission from FR I jets
is therefore not associated with the flattest radio spectra, but with a
particle-acceleration process whose characteristic energy index is 2.24. The
spectral flattening with distance from the nucleus occurs where our
relativistic jet models require deceleration, and the flatter-spectra at the
jet edges may be associated with transverse velocity shear. (Slightly abridged)

Astrophysics