  We have derived long series expansions of the percolation probability for
site and bond percolation on directed square and honeycomb lattices. For the
square bond problem we have extended the series from 41 terms to 54, for the
square site problem from 16 terms to 37, and for the honeycomb bond problem
from 13 terms to 36. Analysis of the series clearly shows that the critical
exponent $\beta$ is the same for all the problems confirming expectations of
universality. For the critical probability and exponent we find in the square
bond case, $q_c = 0.3552994\pm 0.0000010$, $\beta = 0.27643\pm 0.00010$, in the
square site case $q_c = 0.294515 \pm 0.000005$, $\beta = 0.2763 \pm 0.0003$,
and in the honeycomb bond case $q_c = 0.177143 \pm 0.000002$, $\beta = 0.2763
\pm 0.0002$. In addition we have obtained accurate estimates for the critical
amplitudes. In all cases we find that the leading correction to scaling term is
analytic, i.e., the confluent exponent $\Delta = 1$.
