We report 32 statistically significant measurements of the line-of-sig
ht component of the magnetic field strength, B-2, in four diffuse clou
ds, via the Zeeman effect in the 21 cm line of H I. The region near MB
M 27-30 in the Ursa Major complex has B-z > 4 mu G throughout a filame
ntary region 15 pc long, with significant structure on scales as small
as 1.6 pc. The greatest field strength measured in this cloud is 19 /- 2 mu G, greater than in most diffuse clouds by a factor similar to
2. Comparison of measurements with different telescopes suggests that
the field strength at the map peak may be significantly greater than 1
9 mu G On scales smaller than 1.6 pc. The magnetic and kinetic energy
densities M and K in this cloud are comparable, within a factor 2 of 2
x 10(-11) ergs cm(-3) and greater than the gravitational energy densi
ty by a factor similar to 500. Among the four clouds surveyed, six pos
itions where CO emission is a local maximum have essentially the same
mean line-of-sight held strength, B-z approximate to 8 mu G, as do fou
r positions where CO emission is too weak to be detected The similarit
y of M and K in the diffuse clouds discussed here, as well as in dense
r, self-gravitating clouds, suggests strong coupling between magnetic
fields and gas motions in some interstellar clouds, independent of the
ir self-gravity. This coupling probably arises from ion-neutral collis
ions, which allow propagation of MHD waves.