  We present functional versions of recent results on the univariate
distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where
$W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x)
=\inf\{t>0 : W_{t}=-x\}$.
