  We consider an incompressible fluid with axial symmetry without swirl when
the vorticity is sharply concentrated inside $N$ disjoint rings of size
$\varepsilon$ and intensity of the order of $|\log\varepsilon|^{ -1}$. We show
that in the limit $\varepsilon\to 0$ the movement of each vortex ring converges
to a uniform motion along the symmetry axis.
