  The Maskit embedding M of a surface \Sigma is the space of geometrically
finite groups on the boundary of quasifuchsian space for which the `top' end is
homeomorphic to \Sigma, while the `bottom' end consists of two triply punctured
spheres, the remains of \Sigma when two fixed disjoint curves have been
pinched. As such representations vary in the character variety, the conformal
structure on the top side varies over the Teichm\"uller space T(\Sigma).
  We investigate M when \Sigma is a twice punctured torus, using the method of
pleating rays. Fix a projective measure class [\mu] supported on closed curves
on \Sigma. The pleating ray P_[\mu] consists of those groups in M for which the
bending measure of the top component of the convex hull boundary of the
associated 3-manifold is in [\mu]. It is known that P is a real 1-submanifold
of M. Our main result is a formula for the asymptotic direction of P in M as
the bending measure tends to zero, in terms of natural parameters for the
2-complex dimensional representation space R and the Dehn-Thurston coordinates
of the support curves to [\mu] relative to the pinched curves on the bottom
side. This leads to a method of locating M in R.

Geometric Topology