  The two-dimensional site percolation problem is studied by transfer-matrix
methods on finite-width strips with free boundary conditions. The relationship
between correlation-length amplitudes and critical indices, predicted by
conformal invariance, allows a very precise determination of the surface
decay-of-correlations exponent, $\eta_s = 0.6664 \pm 0.0008$, consistent with
the analytical value $\eta_s = 2/3$. It is found that a special transition does
not occur in the case, corroborating earlier series results. At the ordinary
transition, numerical estimates are consistent with the exact value $y_s = -1$
for the irrelevant exponent.
