  In 1996, Kirk Lancaster and David Siegel investigated the existence and
behavior of radial limits at a corner of the boundary of the domain of
solutions of capillary and other prescribed mean curvature problems with
contact angle boundary data. In Theorem 3, they provide an example of a
capillary surface in a unit disk $D$ which has no radial limits at
$(0,0)\in\partial D.$ In their example, the contact angle ($\gamma$) cannot be
bounded away from zero and $\pi.$
  Here we consider a domain $\Omega$ with a convex corner at $(0,0)$ and find a
capillary surface $z=f(x,y)$ in $\Omega\times\mathbb{R}$ which has no radial
limits at $(0,0)\in\partial\Omega$ such that $\gamma$ is bounded away from $0$
and $\pi.$
