  We present optical spectropolarimetry of the nuclei of 36 Seyfert 1 galaxies,
obtained with the William Herschel and the Anglo-Australian Telescopes from
1996 to 1999. In 20 of these, the optical emission from the active nucleus is
intrinsically polarized. We have measured a significant level of polarization
in a further 7 objects but these may be heavily contaminated by Galactic
interstellar polarization. The intrinsically polarized Seyfert 1s exhibit a
variety of characteristics, with the average polarization ranging from < 0.5 to
5 per cent and many showing variations in both the degree and position angle of
polarization across the broad H alpha emission line. We identify a small group
of Seyfert 1s that exhibit polarization properties similar to those of Seyfert
2 galaxies in which polarized broad-lines have been discovered. These objects
represent direct observational evidence that a Seyfert 2-like far-field polar
scattering region is also present in Seyfert 1s. Several other objects have
features that can be explained in terms of equatorial scattering of line
emission from a rotating disk. We propose that much of the diversity in the
polarization properties of Seyfert galaxies can be understood in terms of a
model involving both equatorial and polar scattering, the relative importance
of the two geometries as sources of polarized light being determined
principally by the inclination of the system axis to the line-of-sight.
