  We measure by Monte Carlo simulations $\g_{string}$ for a model of random
surfaces embedded in three dimensional Euclidean space-time. The action of the
string is the usual Polyakov action plus an extrinsic curvature term. The
system undergoes a phase transition at a finite value $\l_c$ of the extrinsic
curvature coupling and at the transition point the numerically measured value
of $\g_{string}(\l_c) \approx 0.27\pm 0.06$. This is consistent with
$\g_{string}(\l_c)=1/4$, i.e. equal to the first of the non-trivial values of
$\g_{string}$ between 0 and $1/2$.
