We have made measurements with the Green Bank 43 m telescope of the Ze
eman effect in the 1665 and 1667 MHz lines of OH toward dark clouds. T
he typical 1 sigma sensitivity was 3 muG. The only certain detection o
f a magnetic field was toward B1, for which we measured a line-of-sigh
t component Absolute value of B cos theta = - 19.1 +/- 3.9 muG. Compar
ison with our earlier measurement of the field toward B1 with the Arec
ibo telescope provided evidence for a 40% enhancement in field strengt
h between the molecular envelope and core of the B1 cloud, which is co
nsistent with quasi-static contraction of the cloud driven by ambipola
r diffusion. Because the Zeeman effect is only sensitive to the line-o
f-sight component of the magnetic field, a statistical analysis of the
detection and upper limits was necessary. This analysis indicated tha
t the total (not line-of-sight) field strength was typically Absolute
value of B almost-equal-to 16 muG toward the central regions of dark c
louds sampled by the Green Bank beam (for which A(v) almost-equal-to 5
mag and n(H) is similar to 10(3) cm-3), which implied that the centra
l regions were approximately magnetically critical. The data were foun
d to be consistent with the hypotheses that (1) dark clouds are in app
roximate virial equilibrium between magnetic and gravitational energy
and (2) the supersonic line widths observed in dark clouds are the res
ult of MHD motions such as Alfven waves. The data were also consistent
with detailed physical models of initially magnetically subcritical c
louds evolving on the ambipolar diffusion time scale.