The Optical Depth to Gravitational Microlensing in the Direction of the Galactic Bulge

We present the analysis of the first two years of the OGLE search for gravitational lenses towards the Galactic bulge. We detected 9 microlensing events in an algorithmic search of $\sim {10}^8$ measurements of $\sim {10}^6$ stars. The characteristic time scales are in the range $8.6<t_0<62$ days, where $t_0=R_E\mathrm{/}V$. The distribution of amplitudes is consistent with theoretical expectation. The stars seem to be drawn at random from the overall distribution of the observed bulge stars. We find that the optical depth to microlensing is larger than $(3.3\pm 1.2)\times {10}^{-6}$, in excess of current theoretical estimates.