  We present detailed scattering models confirming that distinctive variations
in polarization across the broad Halpha line, which are observed in a
significant fraction of Seyfert 1 galaxies, can be understood in terms of a
rotating line-emitting disc surrounded by a co-planar scattering region (the
equatorial scattering region). The predicted polarization properties are:
averaged over wavelength, the position angle of polarization is aligned with
the projected disc rotation axis and hence also with the radio source axis;
(ii) the polarization PA rotates across the line profile, reaching equal but
opposite (relative to the continuum PA) rotations in the blue and red wings;
(iii) the degree of polarization peaks in the line wings and passes through a
minimum in the line core. We identify 11 objects which exhibit these features
to different degrees. In order to reproduce the large amplitude PA rotations
observed in some cases, the scattering region must closely surround the
emission disc and the latter must itself be a relatively narrow annulus --
presumably the Halpha-emitting zone of a larger accretion disc. Asymmetries in
the polarization spectra may be attributable to several possible causes,
including bulk radial infall in the equatorial scattering region, or
contamination by polar scattered light. The broad Halpha lines do not, in
general, exhibit double-peaked profiles, suggesting that a second
Halpha-emitting component of the broad-line region is present, in addition to
the disc.
