  The Liouville map, introduced by Bonahon, assigns to each point in the
Teichm\"uller space a natural Radon measure on the space of geodesics of the
base surface. The Liouville map is real analytic and it even extends to a
holomorphic map of a neighborhood of the Teichm\"uller space in the
Quasi-Fuchsian space of an arbitrary conformally hyperbolic Riemann surface.
The earthquake paths and by their extension quake-bends, introduced by
Thurston, are particularly nice real-analytic and holomorphic paths in the
Teichm\"uller and the Quasi-Fuchsian space, respectively. We find a geometric
expression for the derivative of the Liouville map along earthquake paths.
