  We compare two relationships between quadratic differentials and measured
geodesic laminations on hyperbolic Riemann surfaces (by foliations or complex
projective structures). Each yields a homeomorphism $\ML(S) \to Q(X)$ for any
conformal structure $X$ on a compact surface $S$. The main result is that these
maps are nearly the same, differing by a multiplicative factor of -2 and an
error term of lower order than the maps themselves (which we bound explicitly).
  As an application we show that the Schwarzian derivative of a $\CP^1$
structure with Fuchsian holonomy is close to a $2\pi$-integral Jenkins-Strebel
differential. We also study compactifications of the space of $\CP^1$
structures using the Schwarzian derivative and grafting coordinates; we show
that the natural map between these extends to the boundary of each fiber over
Teichmuller space, and we describe this extension.
