  We start our analysis by deriving a master equation that describes the motion
of a field with arbitrary spin $s$ on a 3-brane embedded in a non-rotating,
uncharged (4+n)-dimensional black hole background. By numerical analysis, we
derive exact results for the greybody factors and emission rates for scalars,
fermions and gauge bosons emitted directly on the brane, for all energy regimes
and for an arbitrary number $n$ of extra dimensions. The relative emissivities
on the brane for different types of particles are computed and their dependence
on the dimensionality of spacetime is demonstrated -- we therefore conclude
that both the amount and the type of radiation emitted can be used for the
determination of $n$ if the Hawking radiation from these black holes is
observed. The emission of scalar modes in the bulk from the same black holes is
also studied and the relative bulk-to-brane energy emissivity is accurately
computed. We demonstrate that this quantity varies considerably with $n$ but
always remains smaller than unity -- this provides firm support to earlier
arguments made by Emparan, Horowitz and Myers.
