  We discuss the connection between the dark radiation on the brane and the
bulk gravitational field in a dilatonic brane world model proposed by Koyama
and Takahashi where the exact solutions for the five dimensional cosmological
perturbations can be obtained analytically. It is shown that the dark radiation
perturbation is related to the non-normalizable Kaluza-Klein (KK) mode of the
bulk perturbations. For the de Sitter brane in the anti-de Sitter bulk, the
squared mass of this KK mode is $2 H^2$ where $H$ is the Hubble parameter on
the brane. This mode is shown to be connected to the excitation of small black
hole in the bulk in the long wavelength limit. The exact solution for an
anisotropic stress on the brane induced by this KK mode is found, which plays
an important role in the calculation of cosmic microwave background radiation
anisotropies in the brane world.
