The large standard deviations from the rotation solution (Eq. 2 (click here))
and the larger than expected 
values leave the
possibilities that either the internal proper motion errors are underestimates
or that a rigid rotation between the proper motion systems is not a sufficient
model. Additionally, the proper motion measurement of some stars may be
corrupted by the presence of unrecognized optical companions.
We now look at these possible causes in turn.
In Sect. 3 we found that we can bring the 
into agreement with
the number of degrees of freedom if we multiply either the H37Cr
errors or our errors by factors between 1.2 and 1.4. Comparing the
standard deviation of the rotation solution Eq. (2 (click here)) (2.7mas/a) to
the quadratically added median internal errors (Bonn proper motions
1.0 mas/a, Hipparcos proper motions 0.9 mas/a, zero point in each field
1.3 mas/a), we find an enhancement factor of 1.44. For comparison,
Hering et al. (1994) determined the rotation from the proper motion
system of a preliminary Hipparcos catalogue to an inertial one using VLA
radio astrometry of 22 radio stars. They found a-posteriori errors of
the rotation angles which are a factor 1.8 larger than the a-priori
errors expected from the internal errors of the proper motions.
The model (1 (click here)) is strictly applicable only if both proper motion systems are regarded as rigid spheres. However, there is the possibility of systematic field-to-field differences, in analogy to the well-known zonal errors in classical astrometry.
Each of our fields has its own systematic zero-point error. In the cases of the extragalactic objects the zero point is defined by a single proper motion (or a handful of proper motions in the fields of M51 and M81), and fully depends on the error of this proper motion. In the fields with calibration via Schmidt plate astrometry the zero point is defined by a large number of galaxies, so systematic errors from individual galaxies should be averaged out to a certain extent. Internal errors of the field zero points range from 0.6 to 2.0mas/a (Table 1 (click here)). One should keep in mind, however, that these values could be underestimates, especially for fields calibrated by a single extragalactic source.
Brosche et al. (1995b)
discuss the
influence of double stars on the proper motion measurements in a
photographic extragalactic link of Hipparcos. They add companions with
a given distribution of separation and magnitude difference to a
subset of the link stars and separate the resulting systems
into different classes according to their influence on proper motion
measurements. 16% of the systems turned out to be of a dangerous
class: they are not recognizable as double either by Hipparcos or from
the ground, but their period is in a range where ground-based proper
motion measurements (with epoch differences of 70-90 years) average
over more than one half of an orbit, while the orbital motion is seen
by Hipparcos (epoch difference 3.5 years) as part of the proper
motion. The mean orbital motion of these stars is
mas/a. Some of these stars may be present among our
link stars, populating the high end of the 
-distribution
and contributing to the larger than expected standard deviations from the
rotation solutions.
One of the stars used by us in the field of M81 shows a highly
significant deviation between the photographically measured proper
motion and the proper motion determined by Hipparcos (
mas/a; Odenkirchen 1996). According to Bernstein (1996, private communication) this star
has an unexpectedly large 
in the Hipparcos reduction without
yielding a double star solution. This could be an example for the
dangerous cases discussed above. A rotation solution without this star
differs from our adopted solution at a 0.03 mas/a level.
Wielen (1995), in comparing preliminary Hipparcos data with the FK5, agrees that undetected astrometric binaries are a major disturbing effect in the comparison of astrometric catalogues.
We conclude that the order of magnitude of the accuracies found here can be explained by known sources of error.
We mention the effects of (variable) structure of the optical counterparts of compact extragalactic radio sources on their positional accuracy, although they are probably too small to influence the present comparison.
Deep imaging reveals the underlying galaxy of some quasars and sometimes
even optical jets (see e.g.\
Benítez et al. 1996 for OJ287). This component is very faint
compared to the dominant core and probably of no relevance for our
photographic plates, which have limiting magnitudes 
. In
addition, effects due to colour differences between core and host
galaxy are minimized, since we used only plates taken in a blue
spectral range for quasar astrometry. Schramm (1988) and Galas (1990)
investigated the effect of quasar host galaxies on the position of the
quasars and found it to be too small to influence the accuracy of an
extragalactic link using these sources.
Takahashi & Kurihara (1993) found systematic changes of the radio
positions of five extragalactic radio sources measured in the CDP VLBI
project. These are caused by systematic changes in the source
structure due to phenomena like outward motion of knots in jets. Over
epoch differences of 
years these changes are seen as apparent
proper motions of up to 0.26mas/a. Since the changes in source
structure persist over time scales of less than 10 years, our proper
motions based on epoch differences of typically 70 years are hardly
affected by this phenomenon.
The radio observations are not of direct relevance to the present
comparison, since we measure the positions of the optical counterparts
of the extragalactic objects. However, the effect of variable source
structure on the position of quasars should be larger in the radio
than in the optical spectral range, since the jet emissions have
radio-optical spectral indices of 
(
) (Begelman et al. 1984), while the compact cores,
generally used in radio-optical link work, have flatter spectral
indices (
) (Bridle & Perley 1984). Therefore, the
contribution of the jet to the total emission is larger in the radio
than in the optical domain, making the optical positions less prone to
effects of source structure. The apparent proper motions found by
Takahashi & Kurihara (1993) are thus upper limits to the effects
expected in optical astrometry.