  Meanders form a set of combinatorial problems concerned with the enumeration
of self-avoiding loops crossing a line through a given number of points, $n$.
Meanders are considered distinct up to any smooth deformation leaving the line
fixed. We use a recently developed algorithm, based on transfer matrix methods,
to enumerate plane meanders. This allows us to calculate the number of closed
meanders up to $n=48$, the number of open meanders up to $n=43$, and the number
of semi-meanders up to $n=45$. The analysis of the series yields accurate
estimates of both the critical point and critical exponent, and shows that a
recent conjecture for the exact value of the semi-meander critical exponent is
unlikely to be correct, while the conjectured exponent value for closed and
open meanders is not inconsistent with the results from the analysis.
