  A scaling relation \rho_s \simeq 35\sigma_{dc}T_c has been observed in the
copper-oxide superconductors, where \rho_s is the strength of the
superconducting condensate, T_c is the critical temperature, and \sigma_{dc} is
the normal-state dc conductivity close to T_c. This scaling relation is
examined within the context of a clean and dirty-limit BCS superconductor.
These limits are well established for an isotropic BCS gap 2\Delta and a
normal-state scattering rate 1/\tau; in the clean limit 1/\tau \ll 2\Delta, and
in the dirty limit 1/\tau > 2\Delta. The dirty limit may also be defined
operationally as the regime where \rho_s varies with 1/\tau. It is shown that
the scaling relation \rho_s \propto \sigma_{dc}T_c is the hallmark of a BCS
system in the dirty-limit. While the gap in the copper-oxide superconductors is
considered to be d-wave with nodes and a gap maximum \Delta_0, if 1/\tau >
2\Delta_0 then the dirty-limit case is preserved. The scaling relation implies
that the copper-oxide superconductors are likely to be in the dirty limit, and
that as a result the energy scale associated with the formation of the
condensate is scaling linearly with T_c. The a-b planes and the c axis also
follow the same scaling relation. It is observed that the scaling behavior for
the dirty limit and the Josephson effect (assuming a BCS formalism) are
essentially identical, suggesting that in some regime these two effects may be
viewed as equivalent. This raises the possibility that electronic
inhomogeneities in the copper-oxygen planes may play an important role in the
nature of the superconductivity in the copper-oxide materials.
