  We have mapped linearly polarized dust emission from the prestellar cores
L1498 and L1517B with the James Clerk Maxwell Telescope (JCMT) using the
Submillimetre Common User Bolometer Array (SCUBA) and its polarimeter SCUBAPOL
at a wavelength of 850um. We use these measurements to determine the
plane-of-sky magnetic field orientation in the cores. In L1498 we see a
magnetic field across the peak of the core that lies at an offset of 19 degrees
to the short axis of the core. This is similar to the offsets seen in previous
observations of prestellar cores. To the southeast of the peak, in the
filamentary tail of the core, we see that the magnetic field has rotated to lie
almost parallel to the long axis of the filament. We hypothesise that the field
in the core may have decoupled from the field in the filament that connects the
core to the rest of the cloud. We use the Chandrasekhar-Fermi (CF) method to
measure the plane-of-sky field strength in the core of L1498 to be 10 +/- 7 uG.
  In L1517B we see a more gradual turn in the field direction from the northern
part of the core to the south. This appears to follow a twist in the filament
in which the core is buried, with the field staying at a roughly constant 25
degree offset to the short axis of the filament, also consistent with previous
observations of prestellar cores. We again use the CF method and calculate the
magnetic field strength in L1517B also to be 30 +/- 10 uG. Both cores appear to
be roughly virialised. Comparison with our previous work on somewhat denser
cores shows that, for the denser cores, thermal and non-thermal (including
magnetic) support are approximately equal, while for the lower density cores
studied here, thermal support dominates.
