  We present the first interferometric polarization map of the W51 e1/e2
molecular cores obtained with the BIMA array at 1.3 mm wavelength with
approximately 3 arcsecond resolution. The polarization angle varies smoothly
across the double cores with an average position angle of 23+-5 degrees for W51
e1 and 15+-7 degrees for W51 e2. The inferred magnetic field direction is
parallel to the minor axis of the double cores, which is consistent with the
theoretical picture that clouds collapse along the field lines. However, the
magnetic field may not determine the axis of angular momentum of these two
cores as the field directions of the two cores significantly differ with the
previously measured directions of rotational axes. The polarization percentage
decreases toward regions with high intensity, suggesting that the dust
alignment efficiency decreases toward high density regions. The field
directions are highly ordered, and the small dispersion of the polarization
angles implies that magnetic fields are strong ($\gtrsim$ 1 mG) and perhaps
dominate turbulence in W51 e1/e2.
