  By considering a continuous pruning procedure on Aldous's Brownian tree, we
construct a random variable $\Theta$ which is distributed, conditionally given
the tree, according to the probability law introduced by Janson as the limit
distribution of the number of cuts needed to isolate the root in a critical
Galton-Watson tree. We also prove that this random variable can be obtained as
the a.s. limit of the number of cuts needed to cut down the subtree of the
continuum tree spanned by $n$ leaves.
