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It has become increasingly clear that understanding the role played by magnetic fields in the evolution of molecular clouds is an essential part of the study of the formation of stars. In order to further this understanding, we have observed the Zeeman effect in the 1420 MHz line of H I using the Very Large Array. The line-of-sight magnetic field (B$_{\rm los}$) in the W 3 complex has been determined independently in the two velocity components at -38 and -46 km/s with a resolution of 25 arcsec and an rms noise of 3 mJy/beam. The rms noise in our maps of B$_{\rm los}$ is typically 5-10 microgauss. The field reversals across the W 3 core in the -38 km/s component, with the field varying from -120 microgauss in the northeast to +220 microgauss in the southwest. This reversal has been modeled as an hourglass magnetic field with a peak strength of about 1 milligauss created by the collapse of the parent molecular cloud. Within the uncertainties of the model, the flux-to-mass ratio appears to be near the magnetically critical value. In the velocity component at -46 km/s, there is a uniform field of about +10 microgauss, except for a ridge of enhanced B$_{\rm los}$ (about +30 microgauss) across the center of the source. There appears to be a correspondence between the the ridge of enhanced B$_{\rm los}$ and enhanced optical depth previously observed in the same area. Both enhancements may be due to shock compression of the gas.
