  Spectrophotometric observation of the gravitationally microlensed quasar
Q2237+0305 during a High Magnification Event (HME) is potentially a very
powerful tool for probing the structure of the quasars accretion disc on scales
of less than 10^-8 arc seconds. How often we can expect to observe a HME is
dependent on the lens system parameters of galactic transverse velocity, mean
microlens mass and the size of the magnified continuum source. We have
previously used published microlensed light-curves to obtain expressions for
the likely-hood of the values for these parameters (Wyithe, Webster & Turner
1999b,2000; Wyithe, Webster, Turner & Mortlock 2000). Here we use this
information to investigate the expected rate of SHMEs. We find the average rate
of SHMEs as well as the number that we can expect to observe over periods of a
decade and of a single observing season. We find that the average SHME rate
summed over all images in Q2237+0305 is 1.5\pm0.6 - 6.3\pm1.3 events per
decade. During the period following a caustic crossing we find that the event
rate in the corresponding image is enhanced by 50-100%, and therefore that the
overall event rate may be higher during these periods.
  From the distribution of events expected during a 6 month period we find that
there is 1 chance in 4-10 of observing a SHME per observing season. The
systematic dependence in these values arises from the different assumptions for
smooth matter content, orientation of the galactic transverse velocity and the
size of photometric error in the monitoring data. The results support continued
monitoring of Q2237+0305 with the aim of obtaining detailed spectroscopic and
photometric observations of a SHME.
