We present 850 µm polarimetry from the James Clerk Maxwell Telescope toward several dense cores within the dark cloud Barnard 1 in Perseus . Significant polarized emission is detected from across the mapped area and is not confined to the locations of bright cores . This indicates the presence of aligned grains and hence a component of the magnetic field in the plane of the sky . Polarization vectors detected away from bright cores are strongly aligned at a position angle of \sim 90 ^ { \circ } ( east of north ) , while vectors associated with bright cores show alignments of varying orientations . There is no direct correlation between the polarization angles measured in earlier optical polarimetry toward Perseus and the polarized submillimeter thermal emission . Depolarization toward high intensities is exhibited , but toward the brightest core reaches a threshold beyond which no further decrease in polarization percentage is measured . The polarized emission data from the interior envelope are compared with previously published OH Zeeman data to estimate the total field strength and orientation under the assumption of a uniform and non-uniform field component in the region . These results are rough estimates only due to the single independent detection of Zeeman splitting toward Barnard 1 . The uniform field component is thus calculated to be { \bf B } _ { 0 } = 31 \mu G [ \pm ( 0.52 \hat { N } -0.01 \hat { E } ) -0.86 \hat { z } ] in the case where we have assumed the ratio of the dispersion of the line-of-sight field to the field strength to be 0.2 .