  Moving mirrors are submitted to reaction forces by vacuum fields. The
motional force is known to vanish for a single mirror uniformly accelerating in
vacuum. We show that inertial forces (proportional to accelerations) arise in
the presence of a second scatterer, exhibiting properties expected for a
relative inertia: the mass corrections depend upon the distance between the
mirrors, and each mirror experiences a force proportional to the acceleration
of the other one. When the two mirrors move with the same acceleration, the
mass correction obtained for the cavity represents the contribution to inertia
of Casimir energy. Accounting for the fact that the cavity moves as a stressed
rigid body, it turns out that this contribution fits Einstein's law of inertia
of energy.
