  Understanding many physical processes in the solar atmosphere requires
determination of the magnetic field in each atmospheric layer. However, direct
measurements of the magnetic field in the Sun's corona are difficult to obtain.
Using observations with the Coronal Multi-channel Polarimeter, we have
determined the spatial distribution of the plasma density in the corona, and
the phase speed of the prevailing transverse magnetohydrodynamic waves within
the plasma. We combine these measurements to map the plane-of-sky component of
the global coronal magnetic field. The derived field strengths in the corona
from 1.05 to 1.35 solar radii are mostly 1-4 Gauss. These results demonstrate
the capability of imaging spectroscopy in coronal magnetic field diagnostics.
