A new and successful attempt to measure magnetic fields in the Milky Way using the 250-ft radio telescope at Jodrell Bank is reported. The measurements were made by observing the Zeeman splitting of the neutral hydrogen line profiles. The strongest indication of Zeeman splitting was shown by the narrow deep feature of Taurus A. This feature has been shown to be double and has been resolved into two absorbing clouds, one having a magnetic field of 2.5 x 10/sup -5/ gauss and the other a magnetic field of 5 x 10/sup -6/ gauss. Similar but weaker Zeeman features were found in the absorption spectra of Cassiopeia A and Cygnus A. The maximum components of the magnetic field seen in the clouds of the Cassiopeia A and Cygnus A directions are about 5 x 10/sup -6/ gauss. Therefore, these results suggest that the general galactic magnetic field is of the order of 5 x 10/sup -6/ gauss. (L.T.W.)