  The effective four-dimensional, linearised gravity for a brane world model
with higher order curvature terms and a bulk scalar field is analysed. Large
and small distance gravitational laws are derived. The model has a single brane
embedded in a five-dimensional bulk spacetime, and the scalar field represents
the dilaton or a moduli field. The quadratic, Gauss-Bonnet curvature term (and
corresponding higher kinetic terms for the scalar) is also included in the bulk
action. It is particularly natural to include such terms in a brane world
model. Boundary terms and junction conditions for the higher order terms are
given.
  The extra terms allow additional solutions of the field equations, which give
better agreement with observational constraints. Brans-Dicke gravity is
obtained on the brane. The scalar and tensor perturbations are affected
differently by the higher gravity terms, and this provides a way for the scalar
modes to be suppressed relative to the tensor ones. Another new (but less
useful) feature is the appearance of instabilities for some parameter ranges.
