  In this paper we describe a function $F_n:{\bf R}_+ \to {\bf R}_{+}$ such
that for any hyperbolic n-manifold $M$ with totally geodesic boundary $\partial
M \neq \emptyset$, the volume of $M$ is equal to the sum of the values of $F_n$
on the {\em orthospectrum} of $M$. We derive an integral formula for $F_n$ in
terms of elementary functions. We use this to give a lower bound for the volume
of a hyperbolic n-manifold with totally geodesic boundary in terms of the area
of the boundary.
