  The strengths of magnetic fields in interstellar gas clouds are obtained
through observations of the circular polarization of spectral line radiation.
Irregularities in this magnetic field may be present due to turbulence, waves
or perhaps other causes, and may play an essential role in the structure and
evolution of the gas clouds. To infer information about these irregularities
from the observational data, we develop statistical relationships between the
rms values of the irregular component of the magnetic field and spatial
variations in the circular polarization of the spectral line radiation. The
irregularities are characterized in analogy with descriptions of
turbulence---by a sum of Fourier waves having a power spectrum with a slope
similar to that of Kolmogorov turbulence. For comparison, we also perform
computations in which turbulent magnetic and velocity fields from
representative MHD simulations by others are utilized. Although the effects of
the variations about the mean value of the magnetic field along the path of a
ray tend to cancel, a significant residual effect in the polarization of the
emergent radiation remains for typical values of the relevant parameters. A map
of observed spectra of the 21 cm line toward Orion A is analyzed and the
results are compared with our calculations in order to infer the strength of
the irregular component of the magnetic field. The rms of the irregular
component is found to be comparable in magnitude to the mean magnetic field
within the cloud. Hence, the turbulent and Alfven velocities should also be
comparable.
