We present the analysis of the light curves of 8.5 million stars observed d
uring two seasons by EROS (Experience de Recherche d'Objets Sombres), in th
e Galactic plane away from the bulge. Three stars have been found that exhi
bit luminosity variations compatible with gravitational microlensing effect
s due to unseen objects. The corresponding optical depth, averaged over fou
r directions, is <(tau)over bar> = 0.38(-0.15)(+0.53): x 10(-6). All three
candidates have long Einstein radius crossing times (similar to :70 to 100
days). For one of them, the lack of evidence for a parallax or a source siz
e effect enabled us to constrain the lens-source configuration. Another can
didate displays a modulation of the magnification, which is compatible with
the lensing of a binary source.
The interpretation of the optical depths inferred from these observations i
s hindered by the imperfect knowledge of the distance to the target stars.
Our measurements are compatible with expectations from simple galactic mode
ls under reasonable assumptions on the target distances.