  Given a compact orientable surface of negative Euler characteristic, there
exists a natural pairing between the Teichmueuller space of the surface and the
set of homotopy classes of simple loops and arcs. The length pairing sends a
hyperbolic metric and a homotopy class of a simple loop or arc to the length of
geodesic in its homotopy class. We study this pairing function using the
Fenchel-Nielsen coordinates on Teichmueller space and the Dehn-Thurston
coordinates on the space of homotopy classes of curve systems. Our main result
establishes Lipschitz type estimates for the length pairing expressed in terms
of these coordinates. As a consequence, we reestablish a result of
Thurston-Bonahon that the length pairing extends to a continuous map from the
product of the Teichmueller space and the space of measured laminations.
