  The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order $\alpha$. We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.
