  We show that a PSL(2;R)-representation of a Fuchsian group induces the
asymptotics of the Reidemeister torsion for the Seifert manifold corresponding
to the euler class of the PSL(2;R)-representation. We also show that the limit
of leading coefficient of the Reidemeister torsion is determined by the euler
class of a PSL(2;R)-representation of a Fuchsian group. In particular, the
leading coefficient of the Reidemeister torsion for the unit tangent bundle
over a two-orbifold converges to $-\chi \log2$ where $\chi$ is the Euler
characteristic of the two-orbifold. We also give a relation between
$\mathbb{Z}_2$-extensions for PSL(2;R)-representations of a Fuchsian group and
the asymptotics of the Reidemeister torsion.
