  We have carried out an extensive survey of magnetic field strengths toward
dark cloud cores in order to test models of star formation: ambipolar-diffusion
driven or turbulence driven. The survey involved $\sim500$ hours of observing
with the Arecibo telescope in order to make sensitive OH Zeeman observations
toward 34 dark cloud cores. Nine new probable detections were achieved at the
2.5-sigma level; the certainty of the detections varies from solid to marginal,
so we discuss each probable detection separately. However, our analysis
includes all the measurements and does not depend on whether each position has
a detection or just a sensitive measurement. Rather, the analysis establishes
mean (or median) values over the set of observed cores for relevant
astrophysical quantities. The results are that the mass-to-flux ratio is
supercritical by $\sim 2$, and that the ratio of turbulent to magnetic energies
is also $\sim 2$. These results are compatible with both models of star
formation. However, these OH Zeeman observations do establish for the first
time on a statistically sound basis the energetic importance of magnetic fields
in dark cloud cores at densities of order $10^{3-4}$ cm$^{-3}$, and they lay
the foundation for further observations that could provide a more definitive
test.
