We compare these two relationships between quadratic differentials and
measured geodesic laminations, each of which yields a homeomorphism
*ML*
(*S*)*Q*(*X*) for each conformal structure *X* on a compact
surface *S*. We show 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 ^{1}
structure with Fuchsian holonomy is close to a 2-integral
Jenkins-Strebel differential. We also study compactifications of the
space of ^{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 Teichmüller space, and we
describe this extension.