We present an analysis of the light curves of 9.1 million stars observed during three seasons by EROS ( Expérience de Recherche d ’ Objets Sombres ) , in the Galactic plane away from the bulge . Seven stars exhibit luminosity variations compatible with gravitational microlensing effects due to unseen objects . The corresponding optical depth , averaged over four directions , is \bar { \tau } = 0.45 ^ { +0.24 } _ { -0.11 } \times 10 ^ { -6 } . While this value is compatible with expectations from simple galactic models under reasonable assumptions on the target distances , we find an excess of events with short timescale towards the direction closest to the Galactic Centre .