  The spherical orthogonal, unitary, and symplectic ensembles (SOE/SUE/SSE)
$S_\beta(N,r)$ consist of $N \times N$ real symmetric, complex hermitian, and
quaternionic self-adjoint matrices of Frobenius norm $r$, made into a
probability space with the uniform measure on the sphere. For each of these
ensembles, we determine the joint eigenvalue distribution for each $N$, and we
prove the empirical spectral measures rapidly converge to the semicircular
distribution as $N \to \infty$. In the unitary case ($\beta=2$), we also find
an explicit formula for the empirical spectral density for each $N$.
