  Newton law arising due to the gravity localized on the general singular brane
embedded in $AdS_5$ bulk is examined in the absence or presence of the 4d
induced Einstein term. For the RS brane, apart from the subleading correction,
Newton potential obeys 4d-type and $5d$-type gravitational law at long- and
short-ranges if it were not for the induced Einstein term. The 4d induced
Einstein term generates an intermediate range at short distance, in which the
$5d$ Newton potential $1/r^2$ emerges. For Neumann brane the long-range
behavior of Newton potential is exponentially suppressed regardless of the
existence of the induced Einstein term. For Dirichlet brane the expression of
Newton potential is dependent on the renormalized coupling constant $v^{ren}$.
At particular value of $v^{ren}$ Newton potential on Dirichlet brane exhibits a
similar behavior to that on RS brane. For other values the long-range behavior
of Newton potential is exponentially suppressed as that in Neumann brane.
