1 Introduction

The variability and proper motion (VPM) survey is a QSO search project that is based on optical long-term variability and non-detectable proper motions. Variability of flux densities and stationarity of positions are two fundamental properties of quasars, and therefore well suited as selection criteria of a QSO search (e.g., Kron & Chiu 1981; Hawkins 1983; Majewski et al. 1991; Véron & Hawkins 1995; Bershady et al. 1998). However, due to the special demands on the number and the time-baseline of the available observations such attempts must be limited to comparatively small and confined areas. We performed the VPM technique in two Schmidt fields of $\sim$10 square degrees each on the basis of a large number of altogether more than 200 digitised Tautenburg Schmidt plates in the B band with a time-baseline of three decades (Meusinger et al. 1997, 2002).

It is not the primary aim of this project to increase the number of known QSOs by an insignificant fraction; the problems of detecting substantial numbers of QSOs have long been overcome. Over the last decade, among others, the Durham/AAT survey (Boyle et al. 1990), the Large Bright Quasar Survey (Hewett et al. 1995), the Edinburgh Quasar Survey (Goldschmidt & Miller 1998), and the Hamburg/ESO survey (Wisotzki et al. 2000) have been completed. Presently, the 2dF Quasar Survey (Croom et al. 2001) and the Sloan Digital Sky Survey (Schneider et al. 2002) are extremely efficient at identifying very large numbers of quasars. The INT Wide Angle Survey (Sharp et al. 2001) is expected to detect a statistically significant sample of high-redshift quasars. Very deep quasar samples were obtained in the Lockman hole via the X-ray satellite ROSAT (Hasinger et al. 1998) and in the optical domain with the Hubble Space Telescope (e.g., Conti et al. 1998), respectively. Further, the VLA FIRST Bright Quasar Survey (e.g., White et al. 2000) will define a radio-selected QSO sample that is competitive in size with current optically selected samples.

Most of the criteria for the selection of QSO candidates rely upon differences in the broad-band spectral energy distribution of QSOs and stars. Despite the large number of QSOs now catalogued, the selection effects of the conventional surveys are not yet fully understood. It is therefore important to perform QSO surveys that are based on different selection methods. The VPM survey does not directly invoke the spectral energy distribution as the primary selection criterion and provides therefore an interesting opportunity to evaluate the selection effects of more conventional optical QSO searches. For instance, a serious question concerns the possible existence of a substantial population of red QSOs. Extinction-reddened QSOs are suggested both from the AGN unification model (e.g., Antonucci 1993; Maiolino 2001) and from the hypothesis of ultra-luminous IR galaxies (ULIRGs) as QSOs in the making (Sanders et al. 1988). The vast majority of catalogued QSOs have uniform spectral energy distributions with a blue continuum and broad absorption lines. Over the last few years, QSOs with extreme red colours have been detected on the basis of their X-ray emission (e.g., Risaliti et al. 2001) or by radio surveys (Webster et al. 1995; Francis et al. 2000; White et al. 2000; Menou et al. 2001; Gregg et al. 2002). The fraction of unusually red objects among the whole QSO population is however unknown. When compared to other optical surveys, the VPM technique has the advantage that it can discover such red QSOs as long as (1.) they are not too faint in the B band and (2.) they are not much less variable than the conventional QSOs.

The VPM survey was started in the high-galactic latitude field around M 3 (Meusinger et al. 1995). Half of this field is covered by the CFHT blue grens survey (e.g., Crampton et al. 1990). The CFHT QSOs could serve as a training set and were used to define the selection thresholds for the VPM survey in such a way that a $\sim$90% completeness is expected up to $B \approx 19.7$. The strategy, the observational material, and the data reduction for the M 3 field were presented in detail in Paper I (Scholz et al. 1997). The procedures and results for the second search field, around M 92, are described in a series of papers (Brunzendorf & Meusinger 2001, 2002; Meusinger & Brunzendorf 2001, 2002). A brief review of the whole VPM project is given by Meusinger et al. (2002). The present paper presents the QSO sample in the M 3 field. In Sect. 2, we briefly discuss the candidate selection. The spectroscopic follow-up observations are described in Sect. 3. Section 4 gives an overview of the properties of the QSO sample. Conclusions are given in Sect. 5. As in the previous papers, we adopt H₀ = 50 km s^-1 Mpc^-1 and q₀=0.