We describe a technique to search for variability in faint X-ray sourc
es, based on Poisson statistics. This is applied to data in the field
of the detached white dwarf binary RE J1629 + 781 which has been obser
ved repeatedly with the ROSAT Position Sensitive Proportional Counter
(PSPC) over a period of 2.5 yr as part of the calibration programme of
the co-aligned extreme ultraviolet (EUV) sensitive Wide Field Camera.
The field contains eight other identified sources comprising four act
ive galactic nuclei (AGN), a LINER, a probable cluster of galaxies and
two stars. Variability is detected in three of the AGN, which all hav
e redshifts between 0.35 and 0.38. The amplitude of variability ranges
between one and three times the mean count rate, but is only detected
on time-scales of less than 3-5 months. No variability is found in th
e fourth AGN which is at a redshift of 1.1, nor in the LINER galaxy, A
rp 185. The X-ray emission from Arp 185 is relatively bright, and the
upper limit to flux variations is 27 per cent of the mean flux. This r
esult is consistent with a non-AGN origin for the X-ray emission from
this galaxy. Variability is detected from one of the identified stars
in the field, of spectral type dM5.5e. No variations were seen in the
flux of the other star (spectral type G) or from the probable cluster
of galaxies.