  Recent observations with the HINODE satellite have found abundant horizontal
magnetic fields in the internetwork quiet Sun. We compare the results on the
horizontal fields with ground-based observations. We obtained 30 sec-integrated
data of quiet Sun on disc centre during a period of very good seeing. The data
have a rms noise in polarization of around 2 10^-4 of the continuum intensity.
The low noise level allowed for an inversion of the spectra. We compare the
inversion results with proxies for the determination of magnetic flux. We
confirm the presence of the horizontal fields in the quiet Sun internetwork,
with voids of some granules extent of nearly zero linear polarization signal.
Voids in the circular polarization signal are only of granular scale. More than
60 % of the surface show polarization signals above four times the rms noise
level. We find that the total magnetic flux contained in the more inclined to
horizontal fields (gamma > 45 deg) is smaller by a factor of around 2 than that
of the less inclined fields. The proxies for flux determination are seen to
suffer from a strong influence of the thermodynamic state of the atmosphere. We
suggest that the difference of the ratio of horizontal to transversal flux
between the ground-based infrared data and the satellite-based visible data is
due to the different formation heights of the respective spectral lines. We
caution that the true amount of magnetic flux cannot be derived directly from
the spectra. For purely horizontal flux, one would need its vertical extension
that has to estimated by an explicit modeling with the observed spectra as
boundary conditions, or has to be taken from MHD simulations.
