  We use the Israel condition to treat carefully the weak-field perturbations
due to the presence of matter on a 3-brane embedded between two regions of
anti-de Sitter (AdS) space with different curvature lengths. A four dimensional
Newton's Law only emerges at distances that are large compared to the AdS
lengths. When a scalar curvature is included in the brane action, however, it
is possible to generate a four dimensional theory of gravity even when one or
both of the AdS lengths is large compared to distances along the brane. In
particular, we provide an example in which the AdS lengths can be larger than
the millimeter experimental bound.
