  We study the convergence and curvature blow up of La Nave and Tian's
continuity method on a generalised Hirzebruch surface. We show that the
Gromov-Hausdorff convergence is similar to that of the Kahler-Ricci flow and
obtain curvature estimates. We also show that a general solution to the
continuity method either exist or all times, or the scalar curvature blows up.
This behavior is known to be exhibited by the Kahler-Ricci flow.
