  Starting with a concise review of quaternionic geometry and quaternion
K{\"a}hler manifolds, we define a transversely quaternion K{\"a}hler foliation.
Then we formulate and prove the foliated versions of the now classical results
of V.Y. Kraines and A Fujiki on the cohomology of quaternion K{\"a}hler
manifolds. Finally, as any orbifold can be realized as the leaf space of a
suitably defined Riemannian foliation we reformulate our results for quaternion
orbifolds.
