  We prove an Atiyah-Bott-Berline-Vergne type localization formula for Killing
foliations in the context of equivariant basic cohomology. As an application,
we localize some Chern-Simons type invariants, for example the volume of
Sasakian manifolds and secondary characteristic classes of Riemannian
foliations, to the union of closed leaves. Various examples are given to
illustrate our method.
