  The existence of Josephson tunneling has been demonstrated between
YBa$_2$Cu$_3$O$_{7-\delta}$ and Pb with the current flowing along the c-axis of
YBa$_2$Cu$_3$O$_{7-\delta}$. This is presumed to come from an s-wave component
of the superconductivity in YBa$_2$Cu$_3$O$_{7-\delta}$, perhaps induced by the
orthorhombic distortion. This hypothesis by itself appears to be in
contradiction with experiments on twinned samples whose tunneling current does
not follow random statistics. We present a theory which depends on a
competition between the intertwin d-wave coupling and a relatively enhanced
s-wave component on the surface. This theory appears to explain, at least
qualitatively, all observations made to date.

Superconductivity