  Different analyses of identical Hinode SOT/SP data of quiet-sun magnetic
fields have in the past led to contradictory answers to the question of whether
the angular distribution of field vectors is preferentially horizontal or
vertical. These answers have been obtained by combining the measured circular
and linear polarizations in different ways to derive the field inclinations. A
problem with these combinations is that the circular and linear polarizations
scale with field strength in profoundly different ways. Here, we avoid these
problems by using an entirely different approach that is based exclusively on
the fundamental symmetry properties of the transverse Zeeman effect for
observations away from the disk center without any dependence on the circular
polarization. Systematic errors are suppressed by the application of a doubly
differential technique with the 5247-5250 \AA\ line pair for observations with
the ZIMPOL-2 imaging polarimeter on the French THEMIS telescope on Tenerife.
This allows us to determine in a model- and resolution-independent way how the
angular distribution of the intranetwork magnetic fields changes from being
preferentially vertical in the lower and middle photosphere to become
preferentially horizontal in the upper photosphere.
