  The goals of this paper are first to describe and then to apply an
ergodic-theoretic generalization of the Siegel integral formula from the
geometry of numbers. The general formula will be seen to serve both as a guide
and as a tool for questions concerning the distribution, in senses to be made
precise, of the set of closed leaves of measured foliations subordinate to
meromorphic quadratic differentials on closed Riemann surfaces.
