  A cylindrical Josephson junction with a spatially dependent Josephson
coupling which averages to zero is studied in order to model the physics of a
disk of d-wave superconductor embedded in a superconducting film of a different
symmetry. It is found that the system always introduces Josepshon vortices in
order to gain energy at the junction. The critical current is calculated. It is
argued that a recent experiment claimed to provide evidence for s-wave
superconductivity in $YBa_2Cu_3O_7$ may also be consistent with d-wave
superconductivity. Figures available from the author on request.
