We have extended the membership investigation of the globular cluster M 5 to fainter stars and to the outer cluster regions by the use of Schmidt plates completely scanned with the APM measuring machine. For our membership study we used a four-dimensional space of proper motions and coordinates and obtained mean absolute proper motions and dispersions for three distribution functions of the cluster stars, near field stars and distant field stars by the maximum likelyhood method. Unless the high accuracy of membership investigations based on proper motion studies from plates with much better astrometric scale and longer epoch differences can not be achieved, we find a correlation of our membership results with the colour-magnitude diagram of the cluster. The reliability of our membership determination is estimated between 70 and 85 per cent from both the statistical contamination with field stars and from an external comparison with the very accurate membership probabilities in the catalogue of bright cluster stars of Rees (1993).
If we compare the mean absolute proper motion of the cluster obtained from
the membership analysis with that determined without the knowledge of
membership probabilities of the stars (Scholz et al. 1996) we mention a
somewhat lower value of 
. This difference can be explained
as a small magnitude dependent systematic error. In Scholz et al. (1996)
only the faint stars were used in the determination of the mean cluster motion
in order to correspond to the magnitude interval of the reference galaxies
and to prevent such magnitude dependent systematic errors.
From the full scans of the different Schmidt plates (5 Tautenburg, 2 Palomar,
1 UKST) with the APM measuring machine we obtained a tidal radius of M 5
. Using the additional information of the
membership determination we determined 
from
the member counts based on the four-dimensional membership analysis (proper
motions and coordinates) and 
from counting the
cluster members determined only from their proper motions. An indication
of a tidal tail as recently discussed by Grillmair et al. (1995) for 12
other globular clusters was found in the counts of the complete scans of 8 different
Schmidt plates used in this project but not confirmed by the member counts.
This is probably caused by the lower magnitude limit (
) of
the membership determination in comparison to the combined counts of the
complete measurements on 8 plates (
).
Acknowledgements
We thank the Tautenburg, Palomar and UKST Observatories for supplying the plates and Mike Irwin for measuring them on the APM. N. Kharchenko thanks the Deutsche Forschungsgemeinschaft for financial support. We thank the referee, Dr. J. Colin for his helpful comments and suggestions.