  It has recently been proposed that the hierarchy problem can be solved by
considering the warped fifth dimension compactified on $S^{1}/Z_{2}$. Many
studies in the context have assumed a particular choice for an integration
constant $\sigma_{0}$ that appears when one solves the five-dimensional
Einstein equation. Since $\sigma_{0}$ is not determined by the boundary
condition of the five-dimensional theory, $\sigma_{0}$ may be regarded as a
gauge degree of freedom in a sense. To this time, all indications are that the
four-dimensional Planck mass depends on $\sigma_{0}$. In this paper, we
carefully investigate the properties of the geometry in the Randall-Sundrum
model, and consider in which location $y$ the four-dimensional Planck mass is
measured. As a result, we find a $\sigma_{0}$-independent relation between the
four-dimensional Planck mass $M_{\rm Pl}$ and five- dimensional fundamental
mass scale $M$, and remarkably enough, we can take $M$ to TeV region when we
consider models with the Standard Model confined on a distant brane. We also
confirm that the physical masses on the distant brane do not depend on
$\sigma_{0}$ by considering a bulk scalar field as an illustrative example. The
resulting mass scale of the Kaluza-Klein modes is on the order of $M$.
