  The EROS-2 project has been designed to search for microlensing events
towards any dense stellar field. The densest parts of the Galactic spiral arms
have been monitored to maximize the microlensing signal expected from the stars
of the Galactic disk and bulge. 12.9 million stars have been monitored during 7
seasons towards 4 directions in the Galactic plane, away from the Galactic
center. A total of 27 microlensing event candidates have been found. Estimates
of the optical depths from the 22 best events are provided. A first order
interpretation shows that simple Galactic models with a standard disk and an
elongated bulge are in agreement with our observations. We find that the
average microlensing optical depth towards the complete EROS-cataloged stars of
the spiral arms is $\bar{\tau} =0.51\pm .13\times 10^{-6}$, a number that is
stable when the selection criteria are moderately varied. As the EROS catalog
is almost complete up to $I_C=18.5$, the optical depth estimated for the
sub-sample of bright target stars with $I_C<18.5$ ($\bar{\tau}=0.39\pm
>.11\times 10^{-6}$) is easier to interpret. The set of microlensing events
that we have observed is consistent with a simple Galactic model. A more
precise interpretation would require either a better knowledge of the distance
distribution of the target stars, or a simulation based on a Galactic model.
For this purpose, we define and discuss the concept of optical depth for a
given catalog or for a limiting magnitude.
