  Random matrix ensembles with orthogonal and unitary symmetry correspond to
the cases of real symmetric and Hermitian random matrices respectively. We show
that the probability density function for the corresponding spacings between
consecutive eigenvalues can be written exactly in the Wigner surmise type form
$a(s) e^{-b(s)}$ for $a$ simply related to a Painlev\'e transcendent and $b$
its anti-derivative. A formula consisting of the sum of two such terms is given
for the symplectic case (Hermitian matrices with real quaternion elements).
