  We consider the process of $n$ Brownian excursions conditioned to be
nonintersecting. We show the distribution functions for the top curve and the
bottom curve are equal to Fredholm determinants whose kernel we give
explicitly. In the simplest case, these determinants are expressible in terms
of Painlev\'{e} V functions. We prove that as $n\to \infty$, the distributional
limit of the bottom curve is the Bessel process with parameter 1/2. (This is
the Bessel process associated with Dyson's Brownian motion.) We apply these
results to study the expected area under the bottom and top curves.
