  We report here observations of the Zeeman effect in the 18-cm lines of OH in
the envelope regions surrounding four molecular cloud cores toward which
detections of B(LOS) have been achieved in the same lines, and evaluate the
ratio of mass to magnetic flux, M/Phi, between the cloud core and envelope.
This relative M/Phi measurement reduces uncertainties in previous studies, such
as the angle between B and the line of sight and the value of [OH/H]. Our
result is that for all four clouds, the ratios R of the core to the envelope
values of M/Phi are less than 1. Stated another way, the ratios R' of the core
to the total cloud M/Phi are less than 1. The extreme case or idealized (no
turbulence) ambipolar diffusion theory of core formation requires the ratio of
the central to total M/Phi to be approximately equal to the inverse of the
original subcritical M/Phi, or R' > 1. The probability that all four of our
clouds have R' > 1 is 3 x 10^{-7}; our results are therefore significantly in
contradiction with the hypothesis that these four cores were formed by
ambipolar diffuson. Highly super-Alfvenic turbulent simulations yield a wide
range of relative M/Phi, but favor a ratio R < 1, as we observe. Our experiment
is limited to four clouds, and we can only directly test the predictions of the
extreme-case "idealized" models of ambipolar-diffusion driven star formation
that have a regular magnetic field morphology. Nonetheless, our experimental
results are not consistent with the "idealized" strong field, ambipolar
diffusion theory of star formation.
