Magnetic fields, pressures, and thermally unstable gas in prominent H I shells

B(parallel) from the Zeeman effect has been measured for the 21 cm line in emission in a number of morphologically prominent H I shells. The H I structures are in fact filamentary instead of sheetlike. B(parallel) is typically about 6.4 micro-G. If estimates of n(H I) are correct, magnetic pressure dominates thermal gas pressure by a factor of about 67, and linewidths are somewhat smaller than the Alfven velocity. B(parallel) as derived from the Zeeman effect does not correlate with Faraday rotation. A similar lack of correlation is found when comparing optical and diffuse synchrotron polarization in the North Polar Spur. Thus, the magnetic field is oriented differently in different types of region, with little if any correlation.