  Marden and Strebel established the Heights Theorem for integrable holomorphic
quadratic differentials on parabolic Riemann surfaces. We extends the validity
of the Heights Theorem to all surfaces whose fundamental group is of the first
kind. In fact, we establish a more general result: the {\it horizontal} map
which assigns to each integrable holomorphic quadratic differential a measured
lamination obtained by straightening the horizontal trajectories of the
quadratic differential is injective for an arbitrary Riemann surface with a
conformal hyperbolic metric. This was established by Strebel in the case of the
unit disk. When a hyperbolic surface has a bounded geodesic pants
decomposition, the horizontal map assigns a bounded measured lamination to each
integrable holomorphic quadratic differential. When surface has a sequence of
closed geodesics whose lengths go to zero, then there exists an integrable
holomorphic quadratic differential whose horizontal measured lamination is not
bounded. We also give a sufficient condition for the non-integrable holomorphic
quadratic differential to give rise to bounded measured laminations.
