  The largest systematic uncertainty present in the analysis of gravitationally
microlensed quasar light curves is that of the galactic transverse velocity. We
describe a method for determining the transverse velocity as well as its
application to published monitoring data of Q2237+0305 (Irwin et al. 1989;
Corrigan et al. 1991; Ostensen et al 1995). We find that while this data
displays strong evidence for microlensing, it limits the transverse velocity to
be < 500 km/sec (for microlens masses of 0.5 solar masses). In addition, by
combining these results with a new method for modelling the microlensing
contribution of stellar proper motions, we find that the masses of microlenses
in Q2237+0305 are consistent with those of low mass stars.
